Mathematical Statistics with Resampling and R

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John Wiley & Sons, Sep 6, 2011 - Mathematics - 418 pages
This book bridges the latest software applications with the benefits of modern resampling techniques

Resampling helps students understand the meaning of sampling distributions, sampling variability, P-values, hypothesis tests, and confidence intervals. This groundbreaking book shows how to apply modern resampling techniques to mathematical statistics. Extensively class-tested to ensure an accessible presentation, Mathematical Statistics with Resampling and R utilizes the powerful and flexible computer language R to underscore the significance and benefits of modern resampling techniques.

The book begins by introducing permutation tests and bootstrap methods, motivating classical inference methods. Striking a balance between theory, computing, and applications, the authors explore additional topics such as:

  • Exploratory data analysis

  • Calculation of sampling distributions

  • The Central Limit Theorem

  • Monte Carlo sampling

  • Maximum likelihood estimation and properties of estimators

  • Confidence intervals and hypothesis tests

  • Regression

  • Bayesian methods

Throughout the book, case studies on diverse subjects such as flight delays, birth weights of babies, and telephone company repair times illustrate the relevance of the real-world applications of the discussed material. Key definitions and theorems of important probability distributions are collected at the end of the book, and a related website is also available, featuring additional material including data sets, R scripts, and helpful teaching hints.

Mathematical Statistics with Resampling and R is an excellent book for courses on mathematical statistics at the upper-undergraduate and graduate levels. It also serves as a valuable reference for applied statisticians working in the areas of business, economics, biostatistics, and public health who utilize resampling methods in their everyday work.

 

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Contents

3
211
Regression
247
Bayesian Methods
301
Additional Topics
327
ImportanceSampling
346
Ratio Estimate for Importance Sampling
352
Importance Sampling in Bayesian Applications
355
Exercises
359
TheHypergeometricDistribution
378
ThePoissonDistribution
379
TheUniformDistribution
381
TheGammaDistribution
382
The ChiSquare Distribution
385
The Students t Distribution
388
The Beta Distribution
390
The F Distribution
391

Appendix A Review of Probability
363
MeanandVariance
364
The Mean of a Sample of Random Variables
366
TheLawofAverages
367
TheNormalDistribution
368
SumsofNormalRandomVariables
369
Higher Moments and the Moment Generating Function
370
Appendix B Probability Distributions
373
TheMultinomialDistribution
374
TheGeometricDistribution
376
TheNegativeBinomialDistribution
377
Exercises
393
Distributions Quick Reference
395
Solutions to OddNumbered Exercises
399
Bibliography
407
Index
413
Preface xiii
419
Exploratory Data Analysis
13
6
135
7
167
Copyright

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About the author (2011)

LAURA CHIHARA, PhD, is Professor of Mathematics at Carleton College. She has extensive experience teaching mathematical statistics and applied regression analysis. She has supervised undergraduates working on statistics projects for local businesses and organizations such as Target Corporation and the Minnesota Pollution Control Agency. Dr. Chihara has experience with S+ and R from her work at Insightful Corporation (formerly MathSoft) and in statistical consulting.

TIM HESTERBERG, PhD, is Senior Ads Quality Statistician at Google. He was a senior research scientist for Insightful Corporation and led the development of S+Resample and other S+ and R software. Dr. Hesterberg has published numerous articles in the areas of bootstrap and related resampling techniques, Monte Carlo simulation methodology, modern regression, tectonic deformation estimation, and electric demand forecasting.

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