An Introduction to Bootstrap Methods With

This book provides both an elementary and a modern introduction to the bootstrap for students who do not have an extensive background in advanced mathematics. It offers reliable, hands-on coverage of the bootstrap's considerable advantages -- as well as its drawbacks. The book outpaces the competition by skillfully presenting results on improved confidence set estimation, estimation of error rates in discriminant analysis, and applications to a wide variety of hypothesis testing and estimation problems. To alert readers to the limitations of the method, the book exhibits counterexamples to the consistency of bootstrap methods. The authors take great care to draw connections between the more traditional resampling methods and the bootstrap, oftentimes displaying helpful computer routines in R. Emphasis throughout the book is on the use of the bootstrap as an exploratory tool including its value in variable selection and other modeling environments.

Michael R. Chernick, PhD, is Manager of Biostatistical Services at Lankenau Institute for Medical Research, where he conducts statistical design and analysis for pharmaceutical research. He has more than thirty years of experience in the application of statistical methods to such areas as medicine, energy, engineering, insurance, and pharmaceuticals. Dr. Chernick is the author of Bootstrap Methods: A Guide for Practitioners and Researchers, Second Edition and The Essentials of Biostatistics for Physicians, Nurses, and Clinicians, and the coauthor of Introductory Biostatistics for the Health Sciences: Modern Applications Including Bootstrap, all published by Wiley. Robert A. LaBudde, PhD, is President of Least Cost Formulations, Ltd., a mathematical software development company that specializes in optimization and process control software for manufacturing companies. He has extensive experience in industry and academia and currently serves as Adjunct Associate Professor in the Department of Mathematics and Statistics at Old Dominion University.

Preface	p. xi
Acknowledgments	p. xv
List of Tables	p. xvii
Introduction	p. 1
Historical Background	p. 1
Definition and Relationship to the Delta Method and Other Resampling Methods	p. 3
Jackknife	p. 6
Delta Method	p. 7
Cross-Validation	p. 7
Subsampling	p. 8
Wide Range of Applications	p. 8
The Bootstrap and the R Language System	p. 10
Historical Notes	p. 25
Exercises	p. 26
References	p. 27
Estimation	p. 30
Estimating Bias	p. 30
Bootstrap Adjustment	p. 30
Error Rate Estimation in Discriminant Analysis	p. 32
Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation	p. 42
Patch Data Example	p. 51
Estimating Location	p. 53
Estimating a Mean	p. 53
Estimating a Median	p. 54
Estimating Dispersion	p. 54
Estimating an Estimate's Standard Error	p. 55
Estimating Interquartile Range	p. 56
Linear Regression	p. 56
Overview	p. 56
Bootstrapping Residuals	p. 57
Bootstrapping Pairs (Response and Predictor Vector)	p. 58
Heteroscedasticity of Variance: The Wild Bootstrap	p. 58
A Special Class of Linear Regression Models: Multivariable Fractional Polynomials	p. 60
Nonlinear Regression	p. 60
Examples of Nonlinear Models	p. 61
A Quasi-Optical Experiment	p. 63
Nonparametric Regression	p. 63
Examples of Nonparametric Regression Models	p. 64
Bootstrap Bagging	p. 66
Historical Notes	p. 67
Exercises	p. 69
References	p. 71
Confidence Intervals	p. 76
Subsampling, Typical Value Theorem, and Efron's Percentile Method	p. 77
Bootstrap-t	p. 79
Iterated Bootstrap	p. 83
Bias-Corrected (BC) Bootstrap	p. 85
BCa and ABC	p. 85
Tilted Bootstrap	p. 88
Variance Estimation with Small Sample Sizes	p. 90
Historical Notes	p. 94
Exercises	p. 96
References	p. 98
Hypothesis Testing	p. 101
Relationship to Confidence Intervals	p. 103
Why Test Hypotheses Differently?	p. 105
Tendril DX Example	p. 106
Klingenberg Example: Binary Dose-Response	p. 108
Historical Notes	p. 109
Exercises	p. 110
References	p. 111
Time Series	p. 113
Forecasting Methods	p. 113
Time Domain Models	p. 114
Can Bootstrapping Improve Prediction Intervals?	p. 115
Model-Based Methods	p. 118
Bootstrapping Stationary Autoregressive Processes	p. 118
Bootstrapping Explosive Autoregressive Processes	p. 123
Bootstrapping Unstable Autoregressive Processes	p. 123
Bootstrapping Stationary ARMA Processes	p. 123
Block Bootstrapping for Stationary Time Series	p. 123
Dependent Wild Bootstrap (DWB)	p. 126
Frequency-Based Approaches for Stationary Time Series	p. 127
Sieve Bootstrap	p. 128
Historical Notes	p. 129
Exercises	p. 131
References	p. 131
Bootstrap Variants	p. 136
Bayesian Bootstrap	p. 137
Smoothed Bootstrap	p. 138
Parametric Bootstrap	p. 139
Double Bootstrap	p. 139
The m-Out-of-n Bootstrap	p. 140
The Wild Bootstrap	p. 141
Historical Notes	p. 141
Exercises	p. 142
References	p. 142
Chapter Special Topics	p. 144
Spatial Data	p. 144
Kriging	p. 144
Asymptotics for Spatial Data	p. 147
Block Bootstrap on Regular Grids	p. 148
Block Bootstrap on Irregular Grids	p. 148
Subset Selection in Regression	p. 148
Gong's Logistic Regression Example	p. 149
Gunter's Qualitative Interaction Example	p. 153
Determining the Number of Distributions in a Mixture	p. 155
Censored Data	p. 157
P-Value Adjustment	p. 158
The Westfall-Young Approach	p. 159
Passive Plus Example	p. 159
Consulting Example	p. 160
Bioequivalence	p. 162
Individual Bioequivalence	p. 162
Population Bioequivalence	p. 165
Process Capability Indices	p. 165
Missing Data	p. 172
Point Processes	p. 174
Bootstrap to Detect Outliers	p. 176
Lattice Variables	p. 177
Covariate Adjustment of Area Under the Curve Estimates for Receiver Operating Characteristic (ROC) Curves	p. 177
Bootstrapping in SAS	p. 179
Historical Notes	p. 182
Exercises	p. 183
References	p. 185
When the Bootstrap is Inconsistent and How to Remedy It	p. 190
Too Small of a Sample Size	p. 191
Distributions with Infinite Second Moments	p. 191
Introduction	p. 191
Example of Inconsistency	p. 192
Remedies	p. 193
Estimating Extreme Values	p. 194
Introduction	p. 194
Example of Inconsistency	p. 194
Remedies	p. 194
Survey Sampling	p. 195
Introduction	p. 195
Example of Inconsistency	p. 195
Remedies	p. 195
m-Dependent Sequences	p. 196
Introduction	p. 196
Example of Inconsistency When Independence Is Assumed	p. 196
Remedy	p. 197
Unstable Autoregressive Processes	p. 197
Introduction	p. 197
Example of Inconsistency	p. 197
Remedies	p. 197
Long-Range Dependence	p. 198
Introduction	p. 198
Example of Inconsistency	p. 198
A Remedy	p. 198
Bootstrap Diagnostics	p. 199
Historical Notes	p. 199
Exercises	p. 201
References	p. 201
Author Index	p. 204
Subject Index	p. 210
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An Introduction to Bootstrap Methods With Applications to R

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