Phyton

Saturday, September 19, 2009

THE SIMPLE LINEAR REGRESSION MODEL WITH EXAMLE

The relationship between a response variable Y and a predictor variable X is postulated as a linear model



where and are constants called the model regression coefficients or parameters, and is a random disturbance or error

The coefficient , called the slope, may be interpreted as the change in Y for unit change in X. The coefficient , called the constant coefficient or intercept, is the predicted value of Y when X = 0.

Generalisation to (1),can be written as



where yi represents the ith value of the response variable Y , xi represents the ith value of the predictor variable X, and represents the error in the approximation

PARAMETER ESTIMATION

Based on the available data, we wish to estimate the parameters and . This is equivalent to finding the straight line that gives the best fit. We estimate the parameters using the popular least squares method, which gives the line that minimizes the sum of squares of the vertical distances from each point to the line. The vertical distances represent the errors in the response variable. These errors can be obtained by rewriting (2) as



The sum of squares of these distances can then be written as



The values of and that minimize are given by



and

Note that we give the formula for before the formula for because, uses .

The estimates , and are called the least squares estimates of and because they are the solution to the least squares method, the intercept and the slope of the line that has the smallest possible sum of squares of the vertical distances from each point to the line. For this reason, the line is called the least squares regression line.

The least squares regression line is given by



For each observation in our data we can compute



These are called the fitted values. Thus, the ith fitted value, is the point on the least squares regression line (7) corresponding to .

The vertical distance corresponding to the ith observation is



These vertical distances are called the ordinary least squares residuals


EXAMPLE:

A study was conducted to determine the effects of sleep deprivation on student's ability to solve problems. The amount of sleep deprivation varied over 8, 12, 16, 20, and 24 hours without sleep. A total of ten subjects participated in the study, two at each deprivation levels. After a specified
sleep deprivation period, each subject was administered a set of simple addition problems, and the number of errors was recorded. The following results were obtained:












Number of errors(y)
Number of hours without sleep
8 8
6 8
6 12
10 12
8 16
14 16
14 20
12 20
16 24
12 24

1. Find the least squares regression model
2. Calculate and interpret the result
3. Does the data present sufficient evidence to conclude that there is relationship between the number of errors and the number of hours without sleep?
4. Find the observed significance level for the test and interpret its value
5. Find the coefficient of determination and interpret its value
6. Find the coefficient of correlation and interpret its value
7. Find the significance level for the regression model and interpret its value.
8. Determine the 95% confidence interval and interpret its value


Solution

Computing the OLS(Ordinary least squares) regression line:

we want an equation of the form:



To find the Least Squares regression line we need to find intercept and slope.

The slope of the line, is computed by below formula:



The intercept of the line, , is computed by this basic formula:


Table 1
















































































































































XYX - Avg of X X^2Y- Avg of YXYPredictedTSS = Y^2

SSE=(Y-Predicted)^2


88-864-2.620.86.86.761.4
86-864-4.636.86.821.160.64
126-416-4.618.48.721.67.29
1210-416-0.62.48.70.361.69
16800-2.6010.66.766.76
1614003.4010.611.5611.56
20144163.413.612.511.562.25
20124161.45.612.51.960.25
24168645.443.214.429.162.56
24128641.411.214.41.965.76









106160106320
152
112.440.2

Using the quantities in Table 1, we have



and

Then the equation of the least squares regression line is

Thursday, August 27, 2009

TeX and LaTeX for PCs






LaTeX is a powerful typesetting system, used for producing scientific and mathematical documents of high typographic quality. Unlike WYSIWYG tools such as FrameMaker and Word,
it uses plain text files that contain formatting commands. It’s big, open source, stable and used
by many technical publishing companies. It’s also relatively unknown in the technical writing
community.

Note: Nearly every serious student of math and Statistics will use LaTeX frequently.

Installing (La)TeX for Free

If you are using a Windows machine, you can download and install the following two programs (MiKTeX and TeXnicCenter, in that order) to get started with LaTeX. These programs are free

Note: These are not the only ways to install and use LaTeX on your computer. The TeX Users Group has a list of other LaTeX programs, including programs for Mac and Linux computers.

MikTeX

MiKTeX is the engine that does the typsetting work.

Note: The MiKTeX download is a large file, about 82.33 MB. If you have a slow internet connection, you may prefer to buy a MiKTeX CD rather than downloading it for free.

To download and install MiKTeX, do the following:

  1. Click here to open the MiKTeX download site in a new window.
  2. Download the basic MiKTeX system by clicking on the link that says Download "Basic MiKTeX" Installer. (This link is listed under the heading "Installing a basic system"). Clicking on that link will open a Download page. Find the 'Location' that's nearest you, then click on the 'Download' link corresponding to that location. A 'File Download' window will probably pop up after a few seconds - choose to Save the file. Pay attention to where you save the file. It doesn't matter where you save it, but you will have to find it later.
  3. After the MiKTeX system download has finished, find the downloaded file, and double-click on it to launch the installer. Follow the directions in the installer. Some things to watch out for while installing:
    • When it askes you for the directory in which to install the files, we recommend leaving the default "C:\Program Files\MiKTeX 2.7", but if you choose to change it, make note of where you change it to: you will need this information when installing TeXnicCenter.
    • It will ask you your "preferred paper size". North American users will probably want "Letter"; most users elsewhere in the world will want "A4".
    • When it asks "Download packages on the fly", we recommend choosing the default "Ask me first".

At this point, MiKTeX should be installed on your computer.

TeXnicCenter

TeXnicCenter is a visual interface and editor for producing LaTeX documents. It is not a "What You See Is What You Get" editor, meaning your code doesn't immediately become nice math images as you type. However, it does include an easy-to-use interface for finding symbol commands, and its text editor is custom-designed to help you avoid syntax errors. To install TeXnicCenter:

  1. Click here to open the TeXnicCenter download site in a new window.
  2. Click on "Downloads" on the left side of the page.
  3. Click on the link next to "TeXnicCenter Setup..." in the "End-User Downloads" section (next the top of the page). (It will probably have a green bar next to it.)
  4. Find the 'Location' that's nearest you, then click on the 'Download' link corresponding to that location. A 'File Download' window will probably pop up after a few seconds - choose to Save the file. Pay attention to where you save the file. It doesn't matter where you save it, but you will have to find it later.
  5. Once the download is finished, run the program that you just downloaded. We recommend accepting the default options, except that you may wish to add a desktop shortcut icon when you are asked.
  6. If you elected to have a shortcut on the desktop, just click the icon on the desktop. Otherwise, click Start on the main Windows window, then 'All Programs', then 'TeXnicCenter', then choose the TeXnicCenter option.
  7. When the program starts, a Tips window will open. Click Close. The program will then walk you through the configuration wizard:
    • When it askes you for the "full path of the directory where the executables" are located, type C:\Program Files\MiKTeX 2.7\miktex\bin (Note: if you changed the default location when installing MiKTeX, then you'll need to replace "C:\Program Files\MiKTeX 2.7" with the directory to which you installed MiKTeX.)
    • If it asks you to pick a PostScript viewer, you may just leave everything blank and just click "Next". Similarly if it asks you to pick a DVI viewer, just leave everything blank and click "Next". (It may or may not ask you these things, depending on how your computer is configured.)






Wednesday, April 15, 2009




1. Advanced Calculus with Applications in Statistics
2.A History of Probability and Statistics and Their Applications before 1750
3.Markov Decision Processes: Discrete Stochastic Dynamic Programming
4.Probability and Statistical Inference
5.Continuous Univariate Distributions, Vol. 1
6.Continuous Univariate Distributions, Vol. 2
7.The Theory of Measures and Integration
8.Robust Statistics: Theory and Methods
9.Finite Mixture Models
10.Generalized, Linear, and Mixed Models
11.Statistics of Extremes: Theory and Applications
12.Modes of Parametric Statistical Inference
13.Univariate Discrete Distributions
14.Contemporary Bayesian Econometrics and Statistics
15.Approximation Theorems of Mathematical Statistics
16.Image Processing and Jump Regression Analysis
17.Operational Risk : Modeling Analytics
18.Design and Analysis of Experiments, Introduction to Experimental Design
19.Introductory Biostatistics for the Health Sciences: Modern Applications Including Bootstrap
20.Linear Models in Statistics
21.Statistics for Research
22.Applied Logistic Regression
23.Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction
24.Probability and Measure, 2nd Edition
25.Theory of Preliminary Test and Stein-Type Estimation with Applications
26.The EM Algorithm and Extensions
27.The Theory of Response-Adaptive Randomization in Clinical Trials
28.Models for Probability and Statistical Inference: Theory and Applications
29.Applied Life Data Analysis
30.Structural Equation Modelling: A Bayesian Approach
31.Bootstrap Methods: A Guide for Practitioners and Researchers
32.Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice
33.Applied Linear Regression, 3rd edition
34.Theory of Probability: A Critical Introductory Treatment
35.Financial Derivatives in Theory and Practice
36.Quantitative Methods in Population Health: Extensions of Ordinary Regression
37.Statistical Methods for Survival Data Analysis
38.Applied Bayesian Modelling
39.Spatial Statistics, 2004-08
40.Approximate Dynamic Programming: Solving the Curses of Dimensionality
41.Variance Components
42.Time Series: Applications to Finance
43.Generalized Least Squares
44.Statistical Analysis With Missing Data
45.Long-Memory Time Series: Theory and Methods
46.Statistical Models and Methods for Lifetime Data
47.Uncertainty Analysis with High Dimensional Dependence Modelling
48.Simulation and the Monte Carlo Method
49.A Matrix Handbook for Statisticians
50.Meta Analysis: A Guide to Calibrating and Combining Statistical Evidence
51.Precedence-Type Tests and Applications
52.Statistical Meta-Analysis with Applications
53.Management of Data in Clinical Trials
54.Periodically Correlated Random Sequences: Spectral Theory and Practice
55.Design and Analysis of Experiments, Advanced Experimental Design
56.Methods and Applications of Linear Models : Regression and the Analysis of Variance
57.Combinatorial Methods in Discrete Distributions
58.Nonparametric Regression Methods for Longitudinal Data Analysis: Mixed-Effects Modeling Approaches
59.Response Surfaces, Mixtures, and Ridge Analyses
60.Variations on Split Plot and Split Block Experiment Designs
61.Recent Advances in Quantitative Methods in Cancer and Human Health Risk Assessment
62.The Construction of Optimal Stated Choice Experiments: Theory and Methods
63.Nonparametric Density Estimation: The L1 View
64.Applied MANOVA and Discriminant Analysis
65.Survey Errors and Survey Costs
66.Statistical Advances in the Biomedical Sciences: Clinical Trials, Epidemiology, Survival Analysis, and Bioinformatics
67.Latent Curve Models: A Structural Equation Perspective
68.Regression Diagnostics: Identifying Influential Data and Sources of Collinearity
69.Reliability and Risk: A Bayesian Perspective
70.Environmental Statistics
71.Bayes Linear Statistics, Theory & Methods
72.Introductory Stochastic Analysis for Finance and Insurance
73.Bayesian Models for Categorical Data
74.Bayesian Statistical Modelling
75.Weibull Models
76.Analysis of Financial Time Series
77.Linear Model Theory: Univariate, Multivariate, and Mixed Models
78.An Introduction to Categorical Data Analysis
79.Bayesian Statistics and Marketing
80.Statistical Shape Analysis
81.Nonparametric Statistics with Applications to Science and Engineering
82.Longitudinal Data Analysis
83.Regression Models for Time Series Analysis
84.Introduction to Nonparametric Regression
85.Statistical Modeling by Wavelets
86.Case Studies in Reliability and Maintenance
87.The Geometry of Random Fields
88.Biostatistics : A Methodology For the Health Sciences
89.Planning, Construction, and Statistical Analysis of Comparative Experiments
90.Statistical Size Distributions in Economics and Actuarial Sciences
91.Modern Experimental Design
92.Comparative Statistical Inference
93.Methods of Multivariate Analysis
94.Robust Statistics
95.Order Statistics
96.Fourier Analysis of Time Series : An Introduction
97.Spatial Statistics 1981-04
98.Clinical Trials : A Methodologic Perspective
99.Numerical Issues in Statistical Computing for the Social Scientist
100.Nonlinear Regression
101.Preparing for the Worst : Incorporating Downside Risk in Stock Market Investments
102.Nonlinear Regression Analysis and Its Applications
103.Mixed Models : Theory and Applications
104.Discrete Distributions : Applications in the Health Sciences
105.Design and Analysis of Clinical Trials : Concepts and Methodologies
106.Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives
107.Flowgraph Models for Multistate Time-–to-Event Data
108.Randomization in Clinical Trials: Theory and Practice
109.Regression With Social Data: Modeling Continuous and Limited Response Variables
110.Regression Analysis by Example
111.Categorical Data Analysis
112.Statistical Methods for Reliability Data
113.Elements of Stochastic Processes Wit
114.Random Graphs for Statistical Pattern Recognition
115.Construction and Assessment of Classification Rules
116.The Statistical Analysis of Failure Time Data
117.Statistical Analysis of Finite Mixture Distributions
118.Modern Applied U-Statistics
119.Applied Multiway Data Analysis























alicelau2172008-10-26 05:03


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Advanced Calculus with Applications in Statistics (Wiley Series in Probability and Statistics)
By André I. Khuri
Publisher: Wiley-Interscience
Number Of Pages: 673
Publication Date: 2002-11-18
Sales Rank: 316939
ISBN / ASIN: 0471391042
EAN: 9780471391043
Binding: Hardcover
Manufacturer: Wiley-Interscience
Studio: Wiley-Interscience
Average Rating:
Total Reviews:
Review
"This is an exceptional book, which I would recommend for anyone beginning a career in statistical research." (Journal of the American Statistical Association, September 2004)
Book Description
Successful track record
No competition
Unique blend of mathematics and statistics
Emphasis on applications
The publisher, John Wiley & Sons
Designed to help motivate the learning of advanced calculus by demonstrating its relevance in the field of statistics. Features detailed coverage of optimization techniques and their applications in statistics. Introduces approximation theory. Each chapter contains a significant amount of examples and exercises as well as additional reading lists. --This text refers to an out of print or unavailable edition of this title.
From the Back Cover
Praise for the First Edition
"An enticing approach to the subject. . . . Students contemplating a career in statistics will acquire a valuable understanding of the underlying structure of statistical theory. . . statisticians should consider purchasing it as an additional reference on advanced calculus."
–Journal of the American Statistical Association
"This book is indeed a pleasure to read. It is simple to understand what the author is attempting to accomplish, and to follow him as he proceeds. . . . I would highly recommend the book for one’s personal collection or suggest your librarian purchase a copy."
–Journal of the Operational Research Society
Knowledge of advanced calculus has become imperative to the understanding of the recent advances in statistical methodology. The First Edition of Advanced Calculus with Applications in Statistics has served as a reliable resource for both practicing statisticians and students alike. In light of the tremendous growth of the field of statistics since the book’s publication, AndrĂ© Khuri has reexamined his popular work and substantially expanded it to provide the most up-to-date and comprehensive coverage of the subject.
Retaining the original’s much-appreciated application-oriented approach, Advanced Calculus with Applications in Statistics, Second Edition supplies a rigorous introduction to the central themes of advanced calculus suitable for both statisticians and mathematicians alike. The Second Edition adds significant new material on:
Basic topological concepts
Orthogonal polynomials
Fourier series
Approximation of integrals
Solutions to selected exercises
The volume’s user-friendly text is notable for its end-of-chapter applications, designed to be flexible enough for both statisticians and mathematicians. Its well thought-out solutions to exercises encourage independent study and reinforce mastery of the content. Any statistician, mathematician, or student wishing to master advanced calculus and its applications in statistics will find this new edition a welcome resource.
About the Author
ANDRÉ I. KHURI, PhD, is a Professor in the Department of Statistics at the University of Florida, Gainesville.
Preface.
1. An Introduction to Set Theory.
2. Basic Concepts in Linear Algebra.
3. Limits and Continuity of Functions.
4. Differentiation.
5. Infinite Sequences and Series.
6. Integration.
7. Multidimensional Calculus.
8. Optimization in Statistics.
9. Approximation of Functions.
10. Orthogonal Polynomials.
11. Fourier Series.
12. Approximation of Integrals.
Appendix. Solutions to Selected Exercises.
General Bibliography.
Index.



















alicelau2172008-10-26 05:06


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A History of Probability and Statistics and Their Applications before 1750 (Wiley Series in Probability and Statistics)
By Anders Hald
Publisher: Wiley-Interscience
Number Of Pages: 608
Publication Date: 1990-01
ISBN-10 / ASIN: 0471502308
ISBN-13 / EAN: 9780471502302
Binding: Hardcover
Product Description:
Evoking the life and works of the great natural philosophers who contributed to the development of probability theory and statistics, this bestseller—now available in paperback--also describes the contemporaneous development and interaction of probability theory (and games of chance), statistics (particularly in astronomy and demography), and life insurance mathematics. To read and enjoy this intellectual history, you need know but little statistics or mathematics.



















alicelau2172008-10-26 05:14


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Markov Decision Processes: Discrete Stochastic Dynamic Programming (Wiley Series in Probability and Statistics)
By Martin L. Puterman
Publisher: Wiley-Interscience
Number Of Pages: 680
Publication Date: 2005-03-03
ISBN-10 / ASIN: 0471727822
ISBN-13 / EAN: 9780471727828
Binding: Paperback
Book Description:
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.
"This text is unique in bringing together so many results hitherto found only in part in other texts and papers. . . . The text is fairly self-contained, inclusive of some basic mathematical results needed, and provides a rich diet of examples, applications, and exercises. The bibliographical material at the end of each chapter is excellent, not only from a historical perspective, but because it is valuable for researchers in acquiring a good perspective of the MDP research potential."
-Zentralblatt fur Mathematik
". . . it is of great value to advanced-level students, researchers, and professional practitioners of this field to have now a complete volume (with more than 600 pages) devoted to this topic. . . . Markov Decision Processes: Discrete Stochastic Dynamic Programming represents an up-to-date, unified, and rigorous treatment of theoretical and computational aspects of discrete-time Markov decision processes."
-Journal of the American Statistical Association



















alicelau2172008-10-26 05:19


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Probability and Statistical Inference (Wiley Series in Probability and Statistics)
By Robert Bartoszynski, Magdalena Niewiadomska-Bugaj
Publisher: Wiley-Interscience
Number Of Pages: 647
Publication Date: 2008-01-02
ISBN-10 / ASIN: 0471696935
ISBN-13 / EAN: 9780471696933
Binding: Hardcover
Book Description:
Probability and Statistical Inference, Second Edition is a user-friendly book that stresses the comprehension of concepts instead of the simple acquisition of a skill or tool. It provides a mathematical framework that permits students to carry out various procedures using any number of computer software packages as opposed to relying on one particular package. Its unique approach to problems allows readers to integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.



















alicelau2172008-10-26 05:22


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Continuous Univariate Distributions, Vol. 1 (Wiley Series in Probability and Statistics)
By Norman L. Johnson, Samuel Kotz, N. Balakrishnan
Publisher: Wiley-Interscience
Number Of Pages: 761
Publication Date: 1994-10
ISBN-10 / ASIN: 0471584959
ISBN-13 / EAN: 9780471584957
Binding: Hardcover



















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Continuous Univariate Distributions, Vol. 2 (Wiley Series in Probability and Statistics)
By Norman L. Johnson, Samuel Kotz, N. Balakrishnan
Publisher: Wiley-Interscience
Number Of Pages: 752
Publication Date: 1995-05-08
ISBN-10 / ASIN: 0471584940
ISBN-13 / EAN: 9780471584940
Binding: Hardcover



















alicelau2172008-10-26 05:28


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The Theory of Measures and Integration (Wiley Series in Probability and Statistics)
By Eric M. Vestrup
Publisher: Wiley-Interscience
Number Of Pages: 594
Publication Date: 2003-09-18
ISBN-10 / ASIN: 0471249777
ISBN-13 / EAN: 9780471249771
Binding: Hardcover
Product Description:
An accessible, clearly organized survey of the basic topics of measure theory for students and researchers in mathematics, statistics, and physics
In order to fully understand and appreciate advanced probability, analysis, and advanced mathematical statistics, a rudimentary knowledge of measure theory and like subjects must first be obtained. The Theory of Measures and Integration illuminates the fundamental ideas of the subject-fascinating in their own right-for both students and researchers, providing a useful theoretical background as well as a solid foundation for further inquiry.
Eric Vestrup's patient and measured text presents the major results of classical measure and integration theory in a clear and rigorous fashion. Besides offering the mainstream fare, the author also offers detailed discussions of extensions, the structure of Borel and Lebesgue sets, set-theoretic considerations, the Riesz representation theorem, and the Hardy-Littlewood theorem, among other topics, employing a clear presentation style that is both evenly paced and user-friendly. Chapters include:
* Measurable Functions
* The Lp Spaces
* The Radon-Nikodym Theorem
* Products of Two Measure Spaces
* Arbitrary Products of Measure Spaces
Sections conclude with exercises that range in difficulty between easy "finger exercises"and substantial and independent points of interest. These more difficult exercises are accompanied by detailed hints and outlines. They demonstrate optional side paths in the subject as well as alternative ways of presenting the mainstream topics.
In writing his proofs and notation, Vestrup targets the person who wants all of the details shown up front. Ideal for graduate students in mathematics, statistics, and physics, as well as strong undergraduates in these disciplines and practicing researchers, The Theory of Measures and Integration proves both an able primary text for a real analysis sequence with a focus on measure theory and a helpful background text for advanced courses in probability and statistics.



















alicelau2172008-10-26 05:31


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Robust Statistics: Theory and Methods (Wiley Series in Probability and Statistics)
By Ricardo A. Maronna,&nbspDouglas R. Martin,&nbspVictor J. Yohai,
Publisher: Wiley
Number Of Pages: 436
Publication Date: 2006-06-13
Sales Rank: 65112
ISBN / ASIN: 0470010924
EAN: 9780470010921
Binding: Hardcover
Book Description:
Classical statistical techniques fail to cope well with deviations from a standard distribution. Robust statistical methods take into account these deviations while estimating the parameters of parametric models, thus increasing the accuracy of the inference. Research into robust methods is flourishing, with new methods being developed and different applications considered.
Robust Statistics sets out to explain the use of robust methods and their theoretical justification. It provides an up-to-date overview of the theory and practical application of the robust statistical methods in regression, multivariate analysis, generalized linear models and time series. This unique book:
Enables the reader to select and use the most appropriate robust method for their particular statistical model.
Features computational algorithms for the core methods.
Covers regression methods for data mining applications.
Includes examples with real data and applications using the S-Plus robust statistics library.
Describes the theoretical and operational aspects of robust methods separately, so the reader can choose to focus on one or the other.
Supported by a supplementary website featuring time-limited S-Plus download, along with datasets and S-Plus code to allow the reader to reproduce the examples given in the book.
Robust Statistics aims to stimulate the use of robust methods as a powerful tool to increase the reliability and accuracy of statistical modelling and data analysis. It is ideal for researchers, practitioners and graduate students of statistics, electrical, chemical and biochemical engineering, and computer vision. There is also much to benefit researchers from other sciences, such as biotechnology, who need to use robust statistical methods in their work.



















alicelau2172008-10-26 05:34


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Finite Mixture Models (Wiley Series in Probability and Statistics)
By Geoffrey McLachlan, David Peel,
Publisher: Wiley-Interscience
Number Of Pages: 456
Publication Date: 2000-10-02
Sales Rank: 648477
ISBN / ASIN: 0471006262
EAN: 9780471006268
Binding: Hardcover
Book Description:
An up-to-date, comprehensive account of major issues in finite mixture modeling
This volume provides an up-to-date account of the theory and applications of modeling via finite mixture distributions. With an emphasis on the applications of mixture models in both mainstream analysis and other areas such as unsupervised pattern recognition, speech recognition, and medical imaging, the book describes the formulations of the finite mixture approach, details its methodology, discusses aspects of its implementation, and illustrates its application in many common statistical contexts.
Major issues discussed in this book include identifiability problems, actual fitting of finite mixtures through use of the EM algorithm, properties of the maximum likelihood estimators so obtained, assessment of the number of components to be used in the mixture, and the applicability of asymptotic theory in providing a basis for the solutions to some of these problems. The author also considers how the EM algorithm can be scaled to handle the fitting of mixture models to very large databases, as in data mining applications. This comprehensive, practical guide:
* Provides more than 800 references-400ublished since 1995
* Includes an appendix listing available mixture software
* Links statistical literature with machine learning and pattern recognition literature
* Contains more than 100 helpful graphs, charts, and tables
Finite Mixture Models is an important resource for both applied and theoretical statisticians as well as for researchers in the many areas in which finite mixture models can be used to analyze data.



















alicelau2172008-10-26 05:38


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Generalized, Linear, and Mixed Models (Wiley Series in Probability and Statistics)
By Charles E. McCulloch, Shayle R. Searle,
Publisher: Wiley-Interscience
Number Of Pages: 358
Publication Date: 2001-01-01
Sales Rank: 312567
ISBN / ASIN: 047119364X
EAN: 9780471193647
Binding: Hardcover
Book Description:
Wiley Series in Probability and Statistics
A modern perspective on mixed models
The availability of powerful computing methods in recent decades has thrust linear and nonlinear mixed models into the mainstream of statistical application. This volume offers a modern perspective on generalized, linear, and mixed models, presenting a unified and accessible treatment of the newest statistical methods for analyzing correlated, nonnormally distributed data.
As a follow-up to Searle's classic, Linear Models, and Variance Components by Searle, Casella, and McCulloch, this new work progresses from the basic one-way classification to generalized linear mixed models. A variety of statistical methods are explained and illustrated, with an emphasis on maximum likelihood and restricted maximum likelihood. An invaluable resource for applied statisticians and industrial practitioners, as well as students interested in the latest results, Generalized, Linear, and Mixed Models features:
* A review of the basics of linear models and linear mixed models
* Descriptions of models for nonnormal data, including generalized linear and nonlinear models
* Analysis and illustration of techniques for a variety of real data sets
* Information on the accommodation of longitudinal data using these models
* Coverage of the prediction of realized values of random effects
* A discussion of the impact of computing issues on mixed models



















alicelau2172008-10-26 05:43


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Statistics of Extremes: Theory and Applications
Author: Jan Beirlant, Jef Caers, Johan Segers, Yuri Goegebeur
Publisher: Wiley, John & Sons, Incorporated
Series: Probability and Statistics Series
ISBN: 0471976474
Summary
Research in the statistical analysis of extreme values has flourished over the past decade: new probability models, inference and data analysis techniques have been introduced; and new application areas have been explored. Statistics of Extremes comprehensively covers a wide range of models and application areas, including risk and insurance: a major area of interest and relevance to extreme value theory. Case studies are introduced providing a good balance of theory and application of each model discussed, incorporating many illustrated examples and plots of data. The last part of the book covers some interesting advanced topics, including time series, regression, multivariate and Bayesian modelling of extremes, the use of which has huge potential.
Table of Contents
1 Why extreme value theory? 11 2 The probabilistic side of extreme value theory 45 3 Away from the maximum 83 4 Tail estimation under pareto-type models 99 5 Tail estimation for all domains of attraction 131 6 Case studies 177 7 Regression analysis 209 8 Multivariate extreme value theory 251 9 Statistics of multivariate extremes 297 10 Extremes of stationary time series 369 11 Bayesian methodology in extreme value statistics 429



















alicelau2172008-10-26 05:47


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Modes of Parametric Statistical Inference (Wiley Series in Probability and Statistics)
By Seymour Geisser,&nbspWesley M. Johnson,
Publisher: Wiley-Interscience
Number Of Pages: 192
Publication Date: 2006-01-17
Sales Rank: 847789
ISBN / ASIN: 0471667269
EAN: 9780471667261
Binding: Hardcover
Book Description:
A fascinating investigation into the foundations of statistical inference
This publication examines the distinct philosophical foundations of different statistical modes of parametric inference. Unlike many other texts that focus on methodology and applications, this book focuses on a rather unique combination of theoretical and foundational aspects that underlie the field of statistical inference. Readers gain a deeper understanding of the evolution and underlying logic of each mode as well as each mode's strengths and weaknesses.
The book begins with fascinating highlights from the history of statistical inference. Readers are given historical examples of statistical reasoning used to address practical problems that arose throughout the centuries. Next, the book goes on to scrutinize four major modes of statistical inference:
* Frequentist
* Likelihood
* Fiducial
* Bayesian
The author provides readers with specific examples and counterexamples of situations and datasets where the modes yield both similar and dissimilar results, including a violation of the likelihood principle in which Bayesian and likelihood methods differ from frequentist methods. Each example is followed by a detailed discussion of why the results may have varied from one mode to another, helping the reader to gain a greater understanding of each mode and how it works. Moreover, the author provides considerable mathematical detail on certain points to highlight key aspects of theoretical development.
The author's writing style and use of examples make the text clear and engaging. This book is fundamental reading for graduate-level students in statistics as well as anyone with an interest in the foundations of statistics and the principles underlying statistical inference, including students in mathematics and the philosophy of science. Readers with a background in theoretical statistics will find the text both accessible and absorbing.



















alicelau2172008-10-26 06:17


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Univariate Discrete Distributions (Wiley Series in Probability and Statistics)
By Norman L. Johnson, Adrienne W. Kemp, Samuel Kotz
Publisher: Wiley-Interscience
Number Of Pages: 672
Publication Date: 2005-08-30
ISBN-10 / ASIN: 0471272469
ISBN-13 / EAN: 9780471272465
Binding: Hardcover
Book Description:
Discover the latest advances in discrete distributions theory
The Third Edition of the critically acclaimed Univariate Discrete Distributions provides a self-contained, systematic treatment of the theory, derivation, and application of probability distributions for count data. Generalized zeta-function and q-series distributions have been added and are covered in detail. New families of distributions, including Lagrangian-type distributions, are integrated into this thoroughly revised and updated text. Additional applications of univariate discrete distributions are explored to demonstrate the flexibility of this powerful method.
A thorough survey of recent statistical literature draws attention to many new distributions and results for the classical distributions. Approximately 450 new references along with several new sections are introduced to reflect the current literature and knowledge of discrete distributions.
Beginning with mathematical, probability, and statistical fundamentals, the authors provide clear coverage of the key topics in the field, including:
* Families of discrete distributions
* Binomial distribution
* Poisson distribution
* Negative binomial distribution
* Hypergeometric distributions
* Logarithmic and Lagrangian distributions
* Mixture distributions
* Stopped-sum distributions
* Matching, occupancy, runs, and q-series distributions
* Parametric regression models and miscellanea
Emphasis continues to be placed on the increasing relevance of Bayesian inference to discrete distribution, especially with regard to the binomial and Poisson distributions. New derivations of discrete distributions via stochastic processes and random walks are introduced without unnecessarily complex discussions of stochastic processes. Throughout the Third Edition, extensive information has been added to reflect the new role of computer-based applications.
With its thorough coverage and balanced presentation of theory and application, this is an excellent and essential reference for statisticians and mathematicians.



















alicelau2172008-10-26 06:20


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Contemporary Bayesian Econometrics and Statistics (Wiley Series in Probability and Statistics)
By John Geweke
Publisher: Wiley-Interscience
Number Of Pages: 320
Publication Date: 2005-09-14
ISBN-10 / ASIN: 0471679321
ISBN-13 / EAN: 9780471679325
Binding: Hardcover
Book Description:
Tools to improve decision making in an imperfect world
This publication provides readers with a thorough understanding of Bayesian analysis that is grounded in the theory of inference and optimal decision making. Contemporary Bayesian Econometrics and Statistics provides readers with state-of-the-art simulation methods and models that are used to solve complex real-world problems. Armed with a strong foundation in both theory and practical problem-solving tools, readers discover how to optimize decision making when faced with problems that involve limited or imperfect data.
The book begins by examining the theoretical and mathematical foundations of Bayesian statistics to help readers understand how and why it is used in problem solving. The author then describes how modern simulation methods make Bayesian approaches practical using widely available mathematical applications software. In addition, the author details how models can be applied to specific problems, including:
Linear models and policy choices
Modeling with latent variables and missing data
Time series models and prediction
Comparison and evaluation of models
The publication has been developed and fine- tuned through a decade of classroom experience, and readers will find the author's approach very engaging and accessible. There are nearly 200 examples and exercises to help readers see how effective use of Bayesian statistics enables them to make optimal decisions. MATLAB® and R computer programs are integrated throughout the book. An accompanying Web site provides readers with computer code for many examples and datasets.
This publication is tailored for research professionals who use econometrics and similar statistical methods in their work. With its emphasis on practical problem solving and extensive use of examples and exercises, this is also an excellent textbook for graduate-level students in a broad range of fields, including economics, statistics, the social sciences, business, and public policy.



















alicelau2172008-10-26 06:22


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http://rapidshare.com/files/142061678/Approximation_Theorems_of_Mathematical_Statistics.rar
Approximation Theorems of Mathematical Statistics (Wiley Series in Probability and Statistics)
By Robert J. Serfling
Publisher: Wiley-Interscience
Number Of Pages: 392
Publication Date: 1980-11
ISBN-10 / ASIN: 0471024031
ISBN-13 / EAN: 9780471024033
Binding: Hardcover
Product Description:
This paperback reprint of one of the best in the field covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized.



















alicelau2172008-10-26 06:36


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Image Processing and Jump Regression Analysis (Wiley Series in Probability and Statistics)
By Peihua Qiu
Publisher: Wiley-Interscience
Number Of Pages: 344
Publication Date: 2005-01-28
ISBN-10 / ASIN: 0471420999
ISBN-13 / EAN: 9780471420996
Binding: Hardcover
Book Description:
Image Processing and Jump Regression Analysis builds a bridge between the worlds of computer graphics and statistics by addressing both the connections and the differences between these two disciplines. The author provides a systematic breakdown of the methodology behind nonparametric jump regression analysis by outlining procedures that are easy to use, simple to compute, and have proven statistical theory behind them. Key topics include conventional smoothing procedures, estimation of jump regression curves, edge detection in image processing, and edge-preserving image restoration, to name a few. With mathematical proofs kept to a minimum, this book is uniquely accessible as a primary text in nonparametric jump regression analysis and image processing as well as a reference on image processing or curve/surface estimation.



















alicelau2172008-10-26 06:41


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http://rapidshare.com/files/67089240/Operational_Risk_Modeling_Analytics_0471760897.rar
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Operational Risk : Modeling Analytics (Wiley Series in Probability and Statistics)
By Harry H. Panjer
Publisher: Wiley-Interscience
Number Of Pages: 448
Publication Date: 2006-07-28
ISBN-10 / ASIN: 0471760897
ISBN-13 / EAN: 9780471760894
Binding: Hardcover
Book Description:
Discover how to optimize business strategies from both qualitative and quantitative points of view
Operational Risk: Modeling Analytics is organized around the principle that the analysis of operational risk consists, in part, of the collection of data and the building of mathematical models to describe risk. This book is designed to provide risk analysts with a framework of the mathematical models and methods used in the measurement and modeling of operational risk in both the banking and insurance sectors.
Beginning with a foundation for operational risk modeling and a focus on the modeling process, the book flows logically to discussion of probabilistic tools for operational risk modeling and statistical methods for calibrating models of operational risk. Exercises are included in chapters involving numerical computations for students' practice and reinforcement of concepts.
Written by Harry Panjer, one of the foremost authorities in the world on risk modeling and its effects in business management, this is the first comprehensive book dedicated to the quantitative assessment of operational risk using the tools of probability, statistics, and actuarial science.
In addition to providing great detail of the many probabilistic and statistical methods used in operational risk, this book features:
* Ample exercises to further elucidate the concepts in the text
* Definitive coverage of distribution functions and related concepts
* Models for the size of losses
* Models for frequency of loss
* Aggregate loss modeling
* Extreme value modeling
* Dependency modeling using copulas
* Statistical methods in model selection and calibration
Assuming no previous expertise in either operational risk terminology or in mathematical statistics, the text is designed for beginning graduate-level courses on risk and operational management or enterprise risk management. This book is also useful as a reference for practitioners in both enterprise risk management and risk and operational management.



















alicelau2172008-10-26 06:45


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http://rapidshare.com/files/99065797/Design_and_Analysis_of_Experiments__Volume_1.rar
Design and Analysis of Experiments, Introduction to Experimental Design (Wiley Series in Probability and Statistics)
By Klaus Hinkelmann, Oscar Kempthorne
Publisher: Wiley-Interscience
Number Of Pages: 631
Publication Date: 2007-12-17
ISBN-10 / ASIN: 0471727563
ISBN-13 / EAN: 9780471727569
Binding: Hardcover
Book Description:
This user-friendly new edition reflects a modern and accessible approach to experimental design and analysis
Design and Analysis of Experiments, Volume 1, Second Edition provides a general introduction to the philosophy, theory, and practice of designing scientific comparative experiments and also details the intricacies that are often encountered throughout the design and analysis processes. With the addition of extensive numerical examples and expanded treatment of key concepts, this book further addresses the needs of practitioners and successfully provides a solid understanding of the relationship between the quality of experimental design and the validity of conclusions.
This Second Edition continues to provide the theoretical basis of the principles of experimental design in conjunction with the statistical framework within which to apply the fundamental concepts. The difference between experimental studies and observational studies is addressed, along with a discussion of the various components of experimental design: the error-control design, the treatment design, and the observation design. A series of error-control designs are presented based on fundamental design principles, such as randomization, local control (blocking), the Latin square principle, the split-unit principle, and the notion of factorial treatment structure. This book also emphasizes the practical aspects of designing and analyzing experiments and features:
Increased coverage of the practical aspects of designing and analyzing experiments, complete with the steps needed to plan and construct an experiment
A case study that explores the various types of interaction between both treatment and blocking factors, and numerical and graphical techniques are provided to analyze and interpret these interactions
Discussion of the important distinctions between two types of blocking factors and their role in the process of drawing statistical inferences from an experiment
A new chapter devoted entirely to repeated measures, highlighting its relationship to split-plot and split-block designs
Numerical examples using SAS® to illustrate the analyses of data from various designs and to construct factorial designs that relate the results to the theoretical derivations
Design and Analysis of Experiments, Volume 1, Second Edition is an ideal textbook for first-year graduate courses in experimental design and also serves as a practical, hands-on reference for statisticians and researchers across a wide array of subject areas, including biological sciences, engineering, medicine, pharmacology, psychology, and business.



















alicelau2172008-10-26 07:34


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http://rapidshare.com/files/5107684/Chernick_Introductory_Biostatistics_for_the_Health_Sciences.djvu
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Introductory Biostatistics for the Health Sciences: Modern Applications Including Bootstrap (Wiley Series in Probability and Statistics)
By Michael R. Chernick, Robert H. Friis
Publisher: Wiley-Interscience
Number Of Pages: 424
Publication Date: 2003-03-17
ISBN-10 / ASIN: 047141137X
ISBN-13 / EAN: 9780471411376
Binding: Hardcover
Product Description:
Accessible to medicine- and/or public policy-related audiences, as well as most statisticians.
Emphasis on outliers is discussed by way of detection and treatment.
Resampling statistics software is incorporated throughout.
Motivating applications are presented in light of honest theory.
Plentiful exercises are sprinkled throughout.
A textbook for an introductory course in statistical methods for undergraduate students in the health sciences who have had high school algebra but not necessarily calculus. A previous statistics course would be helpful but is not necessary.



















alicelau2172008-10-26 07:38


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Linear Models in Statistics (Wiley Series in Probability and Statistics)
By Alvin C. Rencher, G. Bruce Schaalje
Publisher: Wiley-Interscience
Number Of Pages: 672
Publication Date: 2008-01-02
ISBN-10 / ASIN: 0471754986
ISBN-13 / EAN: 9780471754985
Binding: Hardcover
Book Description:
The essential introduction to the theory and application of linear models-now in a valuable new edition
Since most advanced statistical tools are generalizations of the linear model, it is neces-sary to first master the linear model in order to move forward to more advanced concepts. The linear model remains the main tool of the applied statistician and is central to the training of any statistician regardless of whether the focus is applied or theoretical. This completely revised and updated new edition successfully develops the basic theory of linear models for regression, analysis of variance, analysis of covariance, and linear mixed models. Recent advances in the methodology related to linear mixed models, generalized linear models, and the Bayesian linear model are also addressed.
Linear Models in Statistics, Second Edition includes full coverage of advanced topics, such as mixed and generalized linear models, Bayesian linear models, two-way models with empty cells, geometry of least squares, vector-matrix calculus, simultaneous inference, and logistic and nonlinear regression. Algebraic, geometrical, frequentist, and Bayesian approaches to both the inference of linear models and the analysis of variance are also illustrated. Through the expansion of relevant material and the inclusion of the latest technological developments in the field, this book provides readers with the theoretical foundation to correctly interpret computer software output as well as effectively use, customize, and understand linear models.
This modern Second Edition features:
New chapters on Bayesian linear models as well as random and mixed linear models
Expanded discussion of two-way models with empty cells
Additional sections on the geometry of least squares
Updated coverage of simultaneous inference
The book is complemented with easy-to-read proofs, real data sets, and an extensive bibliography. A thorough review of the requisite matrix algebra has been addedfor transitional purposes, and numerous theoretical and applied problems have been incorporated with selected answers provided at the end of the book. A related Web site includes additional data sets and SAS(r) code for all numerical examples.
Linear Model in Statistics, Second Edition is a must-have book for courses in statistics, biostatistics, and mathematics at the upper-undergraduate and graduate levels. It is also an invaluable reference for researchers who need to gain a better understanding of regression and analysis of variance.



















alicelau2172008-10-26 07:42


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http://rapidshare.com/files/3699476/Wiley__2004__Statistics_for_Research__third_edition_.rar
Statistics for Research (Wiley Series in Probability and Statistics) (Hardcover)
by Shirley Dowdy (Author), Stanley Wearden (Author), Daniel Chilko (Author)
Hardcover: 640 pages
Publisher: Wiley-Interscience; 3 Sub edition (February 11, 2004)
Language: English
ISBN-10: 047126735X
ISBN-13: 978-0471267355
Review"The text is easy to read, and students will enjoy the wide range of examples and illustrations…a nice improvement over the first and second editions." (Technometrics, February 2005)
Book Description
Learn how to select the proper statistical procedure and interpret results. A must for those who need a self-teaching text in statistical methods. The Third Edition of this bestselling text brings the methodology up to date in a very practical and accessible way and reflects how the changes in the computing environment have transformed the way statistical analyses are performed today. The authors have made several important and timely revisions, including:
Additional material on probability
New sections on odds ratios, ratio and difference estimations, repeated measure analysis, and logistic regression
Printouts of computer analyses on all complex procedures
An accompanying Website illustrating how to use SAS® and JMP® for all procedures


















alicelau2172008-10-26 07:45


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Applied Logistic Regression (Wiley Series in Probability and Statistics - Applied Probability and Statistics Section)
Summary:
From the reviews of the First Edition.
"An interesting, useful, and well-written book on logistic regression models . . . Hosmer and Lemeshow have used very little mathematics, have presented difficult concepts heuristically and through illustrative examples, and have included references."
—Choice
"Well written, clearly organized, and comprehensive . . . the authors carefully walk the reader through the estimation of interpretation of coefficients from a wide variety of logistic regression models . . . their careful explication of the quantitative re-expression of coefficients from these various models is excellent."
—Contemporary Sociology
"An extremely well-written book that will certainly prove an invaluable acquisition to the practicing statistician who finds other literature on analysis of discrete data hard to follow or heavily theoretical."
—The Statistician
In this revised and updated edition of their popular book, David Hosmer and Stanley Lemeshow continue to provide an amazingly accessible introduction to the logistic regression model while incorporating advances of the last decade, including a variety of software packages for the analysis of data sets. Hosmer and Lemeshow extend the discussion from biostatistics and epidemiology to cutting-edge applications in data mining and machine learning, guiding readers step-by-step through the use of modeling techniques for dichotomous data in diverse fields. Ample new topics and expanded discussions of existing material are accompanied by a wealth of real-world examples-with extensive data sets available over the Internet.



















alicelau2172008-10-26 22:01


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Operational Subjective Statistical Methods: A Mathematical, Philosophical, and Historical Introduction (Wiley Series in Probability and Statistics)
Summary:The mathematical implications of personal beliefs and values in science and commerce
Amid a worldwide resurgence of interest in subjectivist statistical method, this book offers a fresh look at the role of personal judgments in statistical analysis. Frank Lad demonstrates how philosophical attention to meaning provides a sensible assessment of the prospects and procedures of empirical inferential learning.
Operational Subjective Statistical Methods offers a systematic investigation of Bruno de Finetti's theory of probability and logic of uncertainty, which recognizes probability as the measure of personal uncertainty at the heart of its mathematical presentation. It identifies de Finetti's "fundamental theorem of coherent provision" as the unifying structure of probabilistic logic, and highlights the judgment of exchangeability rather than causal independence as the key probabilistic component of statistical inference.
Broad in scope, yet firmly grounded in mathematical detail, this text/reference
Invites readers to address the subjective personalist meaning of probability as motivating the mathematical construction
[*]Contains numerous examples and problems, including computing problems using Matlab, assuming no background in Matlab
[*]Explains how to use the material in three distinct sequential courses in math and statistics, as well as in courses at the graduate level in applied fields
[*]Provides an introductory basis for understanding more complex structures of statistical analysis
Complete with fifty illustrations, Operational Subjective Statistical Methods makes an intriguing discipline accessible to professionals, students, and the interested general reader. It contains a wealth of teaching and research material, and offers profound insight into the relationship between philosophy, faith, and scientific method.



















alicelau2172008-10-26 22:06


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Probability and Measure, 2nd Edition (Wiley Series in Probability and Statistics)
By Patrick Billingsley
Publisher: John Wiley & Sons Inc
Number Of Pages: 636
Publication Date: 1986-03; 2nd Edition
Sales Rank: 1617892
ISBN / ASIN: 0471804789
EAN: 9780471804789
Binding: Hardcover



















alicelau2172008-10-26 22:13


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http://rapidshare.com/files/66948469/Theory_of_Preliminary_Test_and_Stein-Type_Estimation_with_Applications_0471563757.rar
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Theory of Preliminary Test and Stein-Type Estimation with Applications (Wiley Series in Probability and Statistics)
By A. K. Md. Ehsanes Saleh
Publisher: Wiley-Interscience
Number Of Pages: 656
Publication Date: 2006-03-27
ISBN-10 / ASIN: 0471563757
ISBN-13 / EAN: 9780471563754
Binding: Hardcover
Book Description:
Theory of Preliminary Test and Stein-Type Estimation with Applications provides a com-prehensive account of the theory and methods of estimation in a variety of standard models used in applied statistical inference. It is an in-depth introduction to the estimation theory for graduate students, practitioners, and researchers in various fields, such as statistics, engineering, social sciences, and medical sciences. Coverage of the material is designed as a first step in improving the estimates before applying full Bayesian methodology, while problems at the end of each chapter enlarge the scope of the applications.
This book contains clear and detailed coverage of basic terminology related to various topics, including:
* Simple linear model; ANOVA; parallelism model; multiple regression model with non-stochastic and stochastic constraints; regression with autocorrelated errors; ridge regression; and multivariate and discrete data models
* Normal, non-normal, and nonparametric theory of estimation
* Bayes and empirical Bayes methods
* R-estimation and U-statistics
* Confidence set estimation



















alicelau2172008-10-26 22:36


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The EM Algorithm and Extensions (Wiley Series in Probability and Statistics)
By Geoffrey J. McLachlan, Thriyambakam Krishnan
Publisher: Wiley-Interscience
Number Of Pages: 360
Publication Date: 2008-03-14
ISBN-10 / ASIN: 0471201707
ISBN-13 / EAN: 9780471201700
Binding: Hardcover
Product Description:
The EM Algorithm and Extensions remains the only single source to offer a complete and unified treatment of the theory, methodology, and applications of the EM algorithm. The highly applied area of statistics here outlined involves applications in regression, medical imaging, finite mixture analysis, robust statistical modeling, survival analysis, and repeated-measures designs, among other areas. The text includes newly added and updated results on convergence, and new discussion of categorical data, numerical differentiation, and variants of the EM algorithm. It also explores the relationship between the EM algorithm and the Gibbs sampler and Markov Chain Monte Carlo methods.



















alicelau2172008-10-26 23:05


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The Theory of Response-Adaptive Randomization in Clinical Trials (Wiley Series in Probability and Statistics)
By Feifang Hu, William F. Rosenberger
Publisher: Wiley-Interscience
Number Of Pages: 232
Publication Date: 2006-08-18
ISBN-10 / ASIN: 0471653969
ISBN-13 / EAN: 9780471653967
Binding: Hardcover
Product Description:
Presents a firm mathematical basis for the use of response-adaptive randomization procedures in practice
The Theory of Response-Adaptive Randomization in Clinical Trials is the result of the authors' ten-year collaboration as well as their collaborations with other researchers in investigating the important questions regarding response-adaptive randomization in a rigorous mathematical framework. Response-adaptive allocation has a long history in biostatistics literature; however, largely due to the disastrous ECMO trial in the early 1980s, there is a general reluctance to use these procedures.
This timely book represents a mathematically rigorous subdiscipline of experimental design involving randomization and answers fundamental questions, including:
How does response-adaptive randomization affect power?
Can standard inferential tests be applied following response-adaptive randomization?
What is the effect of delayed response?
Which procedure is most appropriate and how can "most appropriate" be quantified?
How can heterogeneity of the patient population be incorporated?
Can response-adaptive randomization be performed with more than two treatments or with continuous responses?
The answers to these questions communicate a thorough understanding of the asymptotic properties of each procedure discussed, including asymptotic normality, consistency, and asymptotic variance of the induced allocation. Topical coverage includes:
The relationship between power and response-adaptive randomization
The general result for determining asymptotically best procedures
Procedures based on urn models
Procedures based on sequential estimation
Implications for the practice of clinical trials
Useful for graduate students in mathematics, statistics, and biostatistics as well as researchers and industrial and academic biostatisticians, this book offers a rigorous treatment of the subject in order to find the optimal procedure to use in practice.



















alicelau2172008-10-26 23:16


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Models for Probability and Statistical Inference: Theory and Applications (Wiley Series in Probability and Statistics)
By James H. Stapleton
Publisher: Wiley-Interscience
Number Of Pages: 464
Publication Date: 2007-12-17
ISBN-10 / ASIN: 0470073721
ISBN-13 / EAN: 9780470073728
Binding: Hardcover
Book Description:
This textbook is an introduction to probability and statistical inference for students. It contains a large amount of figures, with simulations and graphs, produced by the statistical package S-Plus(r), included throughout.
It discusses methods for the computer simulation of observations from specified distributions and provides flexibility for instructors. Each section is followed by a range of problems, from simple to more complex with selected answers.



















alicelau2172008-10-27 00:03


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Applied Life Data Analysis (Wiley Series in Probability and Statistics)
By Wayne B. Nelson
Publisher: Wiley
Number Of Pages: 656
Publication Date: 1982-02
ISBN-10 / ASIN: 0471094587
ISBN-13 / EAN: 9780471094586
Binding: Hardcover
Product Description:
A valuable reference in life data analysis research
Your practical guide to statistical methods for predicting product life and reliability and comparing improvements in product manufacturing, design, and application. Describes the use of graphical methods, the method of maximum likelihood, censored data analysis, linear estimation, prediction methods, and methods for complete, singly censored, multiply censored, interval, and quantalresponse data. Techniques are illustrated with step-by-step, real-data numerical examples. This paperback edition features a new preface and includes a brief survey of commercially available software for the analysis of reliability data.



















alicelau2172008-10-28 08:31


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Structural Equation Modelling: A Bayesian Approach (Wiley Series in Probability and Statistics)
By Sik-Yum Lee
Publisher: Wiley
Number Of Pages: 458
Publication Date: 2007-03-23
ISBN-10 / ASIN: 0470024232
ISBN-13 / EAN: 9780470024232
Binding: Hardcover
Book Description:
Structural equation modeling (SEM) is a powerful multivariate method allowing the evaluation of a series of simultaneous hypotheses about the impacts of latent and manifest variables on other variables, taking measurement errors into account. As SEMs have grown in popularity in recent years, new models and statistical methods have been developed for more accurate analysis of more complex data. A Bayesian approach to SEMs allows the use of prior information resulting in improved parameter estimates, latent variable estimates, and statistics for model comparison, as well as offering more reliable results for smaller samples.
Structural Equation Modeling introduces the Bayesian approach to SEMs, including the selection of prior distributions and data augmentation, and offers an overview of the subject’s recent advances.
Demonstrates how to utilize powerful statistical computing tools, including the Gibbs sampler, the Metropolis-Hasting algorithm, bridge sampling and path sampling to obtain the Bayesian results.
Discusses the Bayes factor and Deviance Information Criterion (DIC) for model comparison.
Includes coverage of complex models, including SEMs with ordered categorical variables, and dichotomous variables, nonlinear SEMs, two-level SEMs, multisample SEMs, mixtures of SEMs, SEMs with missing data, SEMs with variables from an exponential family of distributions, and some of their combinations.
Illustrates the methodology through simulation studies and examples with real data from business management, education, psychology, public health and sociology.
Demonstrates the application of the freely available software WinBUGS via a supplementary website featuring computer code and data sets.
Structural Equation Modeling: A Bayesian Approach is a multi-disciplinary text ideal for researchers and students in many areas, including: statistics, biostatistics, business, education, medicine, psychology, public health and social science.



















alicelau2172008-10-28 08:36


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Bootstrap Methods: A Guide for Practitioners and Researchers (Wiley Series in Probability and Statistics)
By Michael R. Chernick
Publisher: Wiley-Interscience
Number Of Pages: 369
Publication Date: 2007-11-12
ISBN-10 / ASIN: 0471756210
ISBN-13 / EAN: 9780471756217
Binding: Hardcover
Book Description:
This book provides an introduction to the bootstrap, offering reliable, authoritative coverage of the bootstrap's considerable advantages--as well as its drawbacks. This Second Edition takes great care to draw connections between the more traditional resampling methods and the bootstrap and places even more emphasis on the use of the bootstrap as an exploratory tool.



















alicelau2172008-10-28 09:12


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Nonparametric Analysis of Univariate Heavy-Tailed Data: Research and Practice (Wiley Series in Probability and Statistics)
By Natalia Markovich
Publisher: Wiley-Interscience
Number Of Pages: 336
Publication Date: 2007-12-21
ISBN-10 / ASIN: 0470510870
ISBN-13 / EAN: 9780470510872
Binding: Hardcover
Book Description:
Heavy-tailed distributions are typical for phenomena in complex multi-component systems such as biometry, economics, ecological systems, sociology, web access statistics, internet traffic, biblio-metrics, finance and business. The analysis of such distributions requires special methods of estimation due to their specific features. These are not only the slow decay to zero of the tail, but also the violation of Cramer’s condition, possible non-existence of some moments, and sparse observations in the tail of the distribution.
The book focuses on the methods of statistical analysis of heavy-tailed independent identically distributed random variables by empirical samples of moderate sizes. It provides a detailed survey of classical results and recent developments in the theory of nonparametric estimation of the probability density function, the tail index, the hazard rate and the renewal function.
Both asymptotical results, for example convergence rates of the estimates, and results for the samples of moderate sizes supported by Monte-Carlo investigation, are considered. The text is illustrated by the application of the considered methodologies to real data of web traffic measurements.



















alicelau2172008-10-28 09:18


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Applied Linear Regression (Wiley Series in Probability and Statistics)
By Sanford Weisberg
Publisher: Wiley-Interscience
Number Of Pages: 336
Publication Date: 2005-02-11
Sales Rank: 495174
ISBN / ASIN: 0471663794
EAN: 9780471663799
Binding: Hardcover
Book Description
Applied Linear Regression, Third Edition is thoroughly updated to help students master the theory and applications of linear regression modeling. Focusing on model building, assessing fit and reliability, and drawing conclusions, the text demonstrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. To facilitate quick learning, this Third Edition stresses using graphical methods to find appropriate models and to better understand them. In that spirit, most analyses and homework problems use graphs for the discovery of structure as well as for the summarization of results. This text is an excellent tool for learning how to use linear regression analysis techniques to solve and gain insight into real-life problems.



















alicelau2172008-10-28 09:21


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Theory of Probability: A Critical Introductory Treatment (Wiley Series in Probability & Mathematical Statistics)
By Bruno De Finetti
Publisher: John Wiley & Sons
Number Of Pages: 675
Publication Date: 1992-06
ISBN-10 / ASIN: 0471588822
ISBN-13 / EAN: 9780471588825
Binding: Paperback



















alicelau2172008-10-28 09:26


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Financial Derivatives in Theory and Practice (Wiley Series in Probability and Statistics)
By Philip Hunt, Joanne Kennedy
Publisher: Wiley
Number Of Pages: 468
Publication Date: 2004-07-23
ISBN-10 / ASIN: 0470863595
ISBN-13 / EAN: 9780470863596
Binding: Paperback
Product Description:
The term Financial Derivative is a very broad term which has come to mean any financial transaction whose value depends on the underlying value of the asset concerned. Sophisticated statistical modelling of derivatives enables practitioners in the banking industry to reduce financial risk and ultimately increase profits made from these transactions.
The book originally published in March 2000 to widespread acclaim. This revised edition has been updated with minor corrections and new references, and now includes a chapter of exercises and solutions, enabling use as a course text.
Comprehensive introduction to the theory and practice of financial derivatives.
Discusses and elaborates on the theory of interest rate derivatives, an area of increasing interest.
Divided into two self-contained parts – the first concentrating on the theory of stochastic calculus, and the second describes in detail the pricing of a number of different derivatives in practice.
Written by well respected academics with experience in the banking industry.
A valuable text for practitioners in research departments of all banking and finance sectors. Academic researchers and graduate students working in mathematical finance.



















alicelau2172008-10-28 09:30


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Quantitative Methods in Population Health: Extensions of Ordinary Regression (Wiley Series in Probability and Statistics)
By Mari Palta
Publisher: Wiley-Interscience
Number Of Pages: 311
Publication Date: 2003-08-04
ISBN-10 / ASIN: 0471455059
ISBN-13 / EAN: 9780471455059
Binding: Hardcover
Product Description:
Each topic starts with an explanation of the theoretical background necessary to allow full understanding of the technique and to facilitate future learning of more advanced or new methods and software
Explanations are designed to assume as little background in mathematics and statistical theory as possible, except that some knowledge of calculus is necessary for certain parts.
SAS commands are provided for applying the methods. (PROC REG, PROC MIXED, and PROC GENMOD)
All sections contain real life examples, mostly from epidemiologic research
First chapter includes a SAS refresher



















alicelau2172008-10-28 09:33


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Statistical Methods for Survival Data Analysis (Wiley Series in Probability and Statistics)
By Elisa T. Lee, John Wenyu Wang
Publisher: Wiley-Interscience
Number Of Pages: 534
Publication Date: 2003-04-17
ISBN-10 / ASIN: 0471369977
ISBN-13 / EAN: 9780471369974
Binding: Hardcover
Book Description:
Third Edition brings the text up to date with new material and updated references.
New content includes an introduction to left and interval censored data; the log-logistic distribution; estimation procedures for left and interval censored data; parametric methods iwth covariates; Cox's proportional hazards model (including stratification and time-dependent covariates); and multiple responses to the logistic regression model.
Coverage of graphical methods has been deleted.
Large data sets are provided on an FTP site for readers' convenience.
Bibliographic remarks conclude each chapter.



















alicelau2172008-10-28 09:52


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Applied Bayesian Modelling (Wiley Series in Probability and Statistics)
By Peter Congdon
Publisher: Wiley
Number Of Pages: 478
Publication Date: 2003-05-06
ISBN-10 / ASIN: 0471486957
ISBN-13 / EAN: 9780471486954
Binding: Hardcover
Product Description:
The use of Bayesian statistics has grown significantly in recent years, and will undoubtedly continue to do so. Applied Bayesian Modelling is the follow-up to the author’s best selling book, Bayesian Statistical Modelling, and focuses on the potential applications of Bayesian techniques in a wide range of important topics in the social and health sciences. The applications are illustrated through many real-life examples and software implementation in WINBUGS – a popular software package that offers a simplified and flexible approach to statistical modelling. The book gives detailed explanations for each example – explaining fully the choice of model for each particular problem. The book
· Provides a broad and comprehensive account of applied Bayesian modelling.
· Describes a variety of model assessment methods and the flexibility of Bayesian prior specifications.
· Covers many application areas, including panel data models, structural equation and other multivariate structure models, spatial analysis, survival analysis and epidemiology.
· Provides detailed worked examples in WINBUGS to illustrate the practical application of the techniques described. All WINBUGS programs are available from an ftp site.
The book provides a good introduction to Bayesian modelling and data analysis for a wide range of people involved in applied statistical analysis, including researchers and students from statistics, and the health and social sciences. The wealth of examples makes this book an ideal reference for anyone involved in statistical modelling and analysis.



















alicelau2172008-10-28 09:55


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Spatial Statistics (Wiley Series in Probability and Statistics)
By Brian D. Ripley
Publisher: Wiley-Interscience
Number Of Pages: 272
Publication Date: 2004-08-09
ISBN-10 / ASIN: 047169116X
ISBN-13 / EAN: 9780471691167
Binding: Paperback
Product Description:
Presents the first comprehensive guide to the analysis of spatial data. Each chapter covers a particular data format and the associated class of problems, introducing theory, giving computational suggestions, and providing examples. Methods are illustrated by computer-drawn figures. Serves as an introduction to this rapidly growing research area for mathematicians and statisticians, and as a reference to new computer methods for research workers in ecology, geology, archeology, and the earth sciences.



















alicelau2172008-10-28 09:59


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Approximate Dynamic Programming: Solving the Curses of Dimensionality (Wiley Series in Probability and Statistics)
By Warren B. Powell
Publisher: Wiley-Interscience
Number Of Pages: 488
Publication Date: 2007-09-26
ISBN-10 / ASIN: 0470171553
ISBN-13 / EAN: 9780470171554
Binding: Hardcover
Product Description:
A complete and accessible introduction to the real-world applications of approximate dynamic programming
With the growing levels of sophistication in modern-day operations, it is vital for practitioners to understand how to approach, model, and solve complex industrial problems. Approximate Dynamic Programming is a result of the author's decades of experience working in large industrial settings to develop practical and high-quality solutions to problems that involve making decisions in the presence of uncertainty. This groundbreaking book uniquely integrates four distinct disciplines-Markov design processes, mathematical programming, simulation, and statistics-to demonstrate how to successfully model and solve a wide range of real-life problems using the techniques of approximate dynamic programming (ADP). The reader is introduced to the three curses of dimensionality that impact complex problems and is also shown how the post-decision state variable allows for the use of classical algorithmic strategies from operations research to treat complex stochastic optimization problems.
Designed as an introduction and assuming no prior training in dynamic programming of any form, Approximate Dynamic Programming contains dozens of algorithms that are intended to serve as a starting point in the design of practical solutions for real problems. The book provides detailed coverage of implementation challenges including: modeling complex sequential decision processes under uncertainty, identifying robust policies, designing and estimating value function approximations, choosing effective stepsize rules, and resolving convergence issues.
With a focus on modeling and algorithms in conjunction with the language of mainstream operations research, artificial intelligence, and control theory, Approximate Dynamic Programming:
Models complex, high-dimensional problems in a natural and practical way, which draws on years of industrial projects
Introduces and emphasizes the power of estimating a value function around the post-decision state, allowing solution algorithms to be broken down into three fundamental steps: classical simulation, classical optimization, and classical statistics
Presents a thorough discussion of recursive estimation, including fundamental theory and a number of issues that arise in the development of practical algorithms
Offers a variety of methods for approximating dynamic programs that have appeared in previous literature, but that have never been presented in the coherent format of a book
Motivated by examples from modern-day operations research, Approximate Dynamic Programming is an accessible introduction to dynamic modeling and is also a valuable guide for the development of high-quality solutions to problems that exist in operations research and engineering. The clear and precise presentation of the material makes this an appropriate text for advanced undergraduate and beginning graduate courses, while also serving as a reference for researchers and practitioners. A companion Web site is available for readers, which includes additional exercises, solutions to exercises, and data sets to reinforce the book's main concepts.



















alicelau2172008-10-28 10:11


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Variance Components (Wiley Series in Probability and Statistics)
By Shayle R. Searle, George Casella, Charles E. McCulloch
Publisher: Wiley-Interscience
Number Of Pages: 536
Publication Date: 2006-03-24
ISBN-10 / ASIN: 0470009594
ISBN-13 / EAN: 9780470009598
Binding: Paperback
Product Description:
WILEY-INTERSCIENCE PAPERBACK SERIES
The Wiley-Interscience Paperback Series consists of selected books that have been made more accessible to consumers in an effort to increase global appeal and general circulation. With these new unabridged softcover volumes, Wiley hopes to extend the lives of these works by making them available to future generations of statisticians, mathematicians, and scientists.
". . .Variance Components is an excellent book. It is organized and well written, and provides many references to a variety of topics. I recommend it to anyone with interest in linear models."
-Journal of the American Statistical Association
"This book provides a broad coverage of methods for estimating variance components which appeal to students and research workers . . . The authors make an outstanding contribution to teaching and research in the field of variance component estimation."
-Mathematical Reviews
"The authors have done an excellent job in collecting materials on a broad range of topics. Readers will indeed gain from using this book . . . I must say that the authors have done a commendable job in their scholarly presentation."
-Technometrics
This book focuses on summarizing the variability of statistical data known as the analysis of variance table. Penned in a readable style, it provides an up-to-date treatment of research in the area. The book begins with the history of analysis of variance and continues with discussions of balanced data, analysis of variance for unbalanced data, predictions of random variables, hierarchical models and Bayesian estimation, binary and discrete data, and the dispersion mean model.



















alicelau2172008-10-28 10:20


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Time Series: Applications to Finance (Wiley Series in Probability and Statistics)
By Ngai Hang Chan
Publisher: Wiley-Interscience
Number Of Pages: 224
Publication Date: 2002-04-18
ISBN-10 / ASIN: 0471411175
ISBN-13 / EAN: 9780471411178
Binding: Hardcover
Book Description:
Elements of Financial Time Series fills a gap in the market in the area of financial time series analysis by giving both conceptual and practical illustrations. Examples and discussions in the later chapters of the book make recent developments in time series more accessible. Examples from finance are maximized as much as possible throughout the book.
* Full set of exercises is displayed at the end of each chapter.
* First seven chapters cover standard topics in time series at a high-intensity level.
* Recent and timely developments in nonstandard time series techniques are illustrated with real finance examples in detail.
* Examples are systemically illustrated with S-plus with codes and data available on an associated Web site.



















alicelau2172008-10-28 10:22


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Generalized Least Squares (Wiley Series in Probability and Statistics)
By Takeaki Kariya, Hiroshi Kurata
Publisher: Wiley
Number Of Pages: 312
Publication Date: 2004-08-13
ISBN-10 / ASIN: 0470866977
ISBN-13 / EAN: 9780470866979
Binding: Hardcover
Product Description:
Generalised Least Squares adopts a concise and mathematically rigorous approach. It will provide an up-to-date self-contained introduction to the unified theory of generalized least squares estimations, adopting a concise and mathematically rigorous approach. The book covers in depth the 'lower and upper bounds approach', pioneered by the first author, which is widely regarded as a very powerful and useful tool for generalized least squares estimation, helping the reader develop their understanding of the theory. The book also contains exercises at the end of each chapter and applications to statistics, econometrics, and biometrics, enabling use for self-study or as a course text.



















alicelau2172008-10-28 10:26


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Statistical Analysis With Missing Data (Wiley Series in Probability and Mathematical Statistics)
By Roderick J.A. Little, Donald B. Rubin
Publisher: Wiley John & Sons
Number Of Pages: 304
Publication Date: 1987-04
ISBN-10 / ASIN: 0471802549
ISBN-13 / EAN: 9780471802549
Binding: Hardcover
Product Description:
* Emphasizes the latest trends in the field.
* Includes a new chapter on evolving methods.
* Provides updated or revised material in most of the chapters.


















alicelau2172008-10-28 10:52


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Long-Memory Time Series: Theory and Methods (Wiley Series in Probability and Statistics)
By Wilfredo Palma
Publisher: Wiley-Interscience
Number Of Pages: 304
Publication Date: 2007-03-30
ISBN-10 / ASIN: 0470114029
ISBN-13 / EAN: 9780470114025
Binding: Hardcover
Book Description:
During the last decades long-memory processes have evolved as a vital and important part of time series analysis. This book attempts to give an overview of the theory and methods developed to deal with long-range dependent data as well as describe some applications of these methodologies to real-life time series. The topics are systematically organized in a progressive manner, starting from foundations (the first three chapters), progressing to the analysis of methodological implications (the next six chapters), and finally extending to more complex long-range dependent data structures (the final three chapters).



















alicelau2172008-10-28 11:03


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Statistical Models and Methods for Lifetime Data (Wiley Series in Probability and Statistics)
By Jerald F. Lawless
Publisher: Wiley-Interscience
Number Of Pages: 664
Publication Date: 2002-11-27
ISBN-10 / ASIN: 0471372153
ISBN-13 / EAN: 9780471372158
Binding: Hardcover
Book Description:
Praise for the First Edition
"An indispensable addition to any serious collection on lifetime data analysis and . . . a valuable contribution to the statistical literature. Highly recommended . . ."
-Choice
"This is an important book, which will appeal to statisticians working on survival analysis problems."
-Biometrics
"A thorough, unified treatment of statistical models and methods used in the analysis of lifetime data . . . this is a highly competent and agreeable statistical textbook."
-Statistics in Medicine
The statistical analysis of lifetime or response time data is a key tool in engineering, medicine, and many other scientific and technological areas. This book provides a unified treatment of the models and statistical methods used to analyze lifetime data.
Equally useful as a reference for individuals interested in the analysis of lifetime data and as a text for advanced students, Statistical Models and Methods for Lifetime Data, Second Edition provides broad coverage of the area without concentrating on any single field of application. Extensive illustrations and examples drawn from engineering and the biomedical sciences provide readers with a clear understanding of key concepts.
New and expanded coverage in this edition includes:
* Observation schemes for lifetime data
* Multiple failure modes
* Counting process-martingale tools
* Both special lifetime data and general optimization software
* Mixture models
* Treatment of interval-censored and truncated data
* Multivariate lifetimes and event history models
* Resampling and simulation methodology



















alicelau2172008-10-28 11:10


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Uncertainty Analysis with High Dimensional Dependence Modelling (Wiley Series in Probability and Statistics)
By Dorota Kurowicka, Roger Cooke
Publisher: Wiley
Number Of Pages: 302
Publication Date: 2006-04-21
ISBN-10 / ASIN: 0470863064
ISBN-13 / EAN: 9780470863060
Binding: Hardcover
Book Description:
Mathematical models are used to simulate complex real-world phenomena in many areas of science and technology. Large complex models typically require inputs whose values are not known with certainty. Uncertainty analysis aims to quantify the overall uncertainty within a model, in order to support problem owners in model-based decision-making. In recent years there has been an explosion of interest in uncertainty analysis. Uncertainty and dependence elicitation, dependence modelling, model inference, efficient sampling, screening and sensitivity analysis, and probabilistic inversion are among the active research areas. This text provides both the mathematical foundations and practical applications in this rapidly expanding area, including:
An up-to-date, comprehensive overview of the foundations and applications of uncertainty analysis.
All the key topics, including uncertainty elicitation, dependence modelling, sensitivity analysis and probabilistic inversion.
Numerous worked examples and applications.
Workbook problems, enabling use for teaching.
Software support for the examples, using UNICORN - a Windows-based uncertainty modelling package developed by the authors.
A website featuring a version of the UNICORN software tailored specifically for the book, as well as computer programs and data sets to support the examples.
Uncertainty Analysis with High Dimensional Dependence Modelling offers a comprehensive exploration of a new emerging field. It will prove an invaluable text for researches, practitioners and graduate students in areas ranging from statistics and engineering to reliability and environmetrics.



















alicelau2172008-10-28 11:14


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Simulation and the Monte Carlo Method (Wiley Series in Probability and Statistics)
By Reuven Y. Rubinstein, Dirk P. Kroese
Publisher: Wiley-Interscience
Number Of Pages: 345
Publication Date: 2007-12-19
ISBN-10 / ASIN: 0470177942
ISBN-13 / EAN: 9780470177945
Binding: Hardcover
Book Description:
* The authoritative resource for understanding the power behind Monte Carlo Methods.
* Most ideas are introduced and explained by way of concrete examples, algorithms, and practical experiments
* A new co-author has now been added to enliven the writing style and to provide modern day expertise on new topics
* An extensive range of exercises is provided at the end of each chapter, with more difficult sections and exercises marked accordingly
* Examples of cross-entropy programs, written in MATLAB, are given in an appendix



















alicelau2172008-10-28 11:19


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A Matrix Handbook for Statisticians (Wiley Series in Probability and Statistics)
By George A. F. Seber
Publisher: Wiley-Interscience
Number Of Pages: 559
Publication Date: 2007-11-27
ISBN-10 / ASIN: 0471748692
ISBN-13 / EAN: 9780471748694
Binding: Hardcover
Book Description:
A comprehensive, must-have handbook of matrix methods with a unique emphasis on statistical applications
This timely book, A Matrix Handbook for Statisticians, provides a comprehensive, encyclopedic treatment of matrices as they relate to both statistical concepts and methodologies. Written by an experienced authority on matrices and statistical theory, this handbook is organized by topic rather than mathematical developments and includes numerous references to both the theory behind the methods and the applications of the methods. A uniform approach is applied to each chapter, which contains four parts: a definition followed by a list of results; a short list of references to related topics in the book; one or more references to proofs; and references to applications. The use of extensive cross-referencing to topics within the book and external referencing to proofs allows for definitions to be located easily as well as interrelationships among subject areas to be recognized.
A Matrix Handbook for Statisticians addresses the need for matrix theory topics to be presented together in one book and features a collection of topics not found elsewhere under one cover. These topics include:
Complex matrices
A wide range of special matrices and their properties
Special products and operators, such as the Kronecker product
Partitioned and patterned matrices
Matrix analysis and approximation
Matrix optimization
Majorization
Random vectors and matrices
Inequalities, such as probabilistic inequalities
Additional topics, such as rank, eigenvalues, determinants, norms, generalized inverses, linear and quadratic equations, differentiation, and Jacobians, are also included. The book assumes a fundamental knowledge of vectors and matrices, maintains a reasonable level of abstraction when appropriate, and provides a comprehensive compendium of linear algebra results with use or potential use in statistics. A Matrix Handbook for Statisticians is an essential, one-of-a-kind book for graduate-level courses in advanced statistical studies including linear and nonlinear models, multivariate analysis, and statistical computing. It also serves as an excellent self-study guide for statistical researchers.