COPYRIGHTED MATERIAL CONTENTS

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1 PREFACE ACKNOWLEDGMENTS LIST OF TABLES xi xv xvii 1 INTRODUCTION Historical Background Definition and Relationship to the Delta Method and Other Resampling Methods Jackknife Delta Method Cross-Validation Subsampling Wide Range of Applications The Bootstrap and the R Language System Historical Notes Exercises 26 References 27 2 ESTIMATION Estimating Bias Bootstrap Adjustment Error Rate Estimation in Discriminant Analysis Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation Patch Data Example Estimating Location Estimating a Mean Estimating a Median Estimating Dispersion Estimating an Estimate s Standard Error Estimating Interquartile Range 56 COPYRIGHTED MATERIAL v

2 vi 2.4 Linear Regression Overview Bootstrapping Residuals Bootstrapping Pairs (Response and Predictor Vector) Heteroscedasticity of Variance: The Wild Bootstrap A Special Class of Linear Regression Models: Multivariable Fractional Polynomials Nonlinear Regression Examples of Nonlinear Models A Quasi-Optical Experiment Nonparametric Regression Examples of Nonparametric Regression Models Bootstrap Bagging Historical Notes Exercises 69 References 71 3 CONFIDENCE INTERVALS Subsampling, Typical Value Theorem, and Efron s Percentile Method Bootstrap-t Iterated Bootstrap Bias-Corrected (BC) Bootstrap BCa and ABC Tilted Bootstrap Variance Estimation with Small Sample Sizes Historical Notes Exercises 96 References 98 4 HYPOTHESIS TESTING Relationship to Confidence Intervals Why Test Hypotheses Differently? Tendril DX Example Klingenberg Example: Binary Dose Response Historical Notes Exercises 110 References 111

3 vii 5 TIME SERIES Forecasting Methods Time Domain Models Can Bootstrapping Improve Prediction Intervals? Model-Based Methods Bootstrapping Stationary Autoregressive Processes Bootstrapping Explosive Autoregressive Processes Bootstrapping Unstable Autoregressive Processes Bootstrapping Stationary ARMA Processes Block Bootstrapping for Stationary Time Series Dependent Wild Bootstrap (DWB) Frequency-Based Approaches for Stationary Time Series Sieve Bootstrap Historical Notes Exercises 131 References BOOTSTRAP VARIANTS Bayesian Bootstrap Smoothed Bootstrap Parametric Bootstrap Double Bootstrap The m-out-of-n Bootstrap The Wild Bootstrap Historical Notes Exercises 142 References CHAPTER SPECIAL TOPICS Spatial Data Kriging Asymptotics for Spatial Data Block Bootstrap on Regular Grids Block Bootstrap on Irregular Grids Subset Selection in Regression Gong s Logistic Regression Example Gunter s Qualitative Interaction Example Determining the Number of Distributions in a Mixture 155

4 viii 7.4 Censored Data P-Value Adjustment The Westfall Young Approach Passive Plus Example Consulting Example Bioequivalence Individual Bioequivalence Population Bioequivalence Process Capability Indices Missing Data Point Processes Bootstrap to Detect Outliers Lattice Variables Covariate Adjustment of Area Under the Curve Estimates for Receiver Operating Characteristic (ROC) Curves Bootstrapping in SAS Historical Notes Exercises 183 References WHEN THE BOOTSTRAP IS INCONSISTENT AND HOW TO REMEDY IT Too Small of a Sample Size Distributions with Infinite Second Moments Introduction Example of Inconsistency Remedies Estimating Extreme Values Introduction Example of Inconsistency Remedies Survey Sampling Introduction Example of Inconsistency Remedies m-dependent Sequences Introduction Example of Inconsistency When Independence Is Assumed Remedy 197

5 ix 8.6 Unstable Autoregressive Processes Introduction Example of Inconsistency Remedies Long-Range Dependence Introduction Example of Inconsistency A Remedy Bootstrap Diagnostics Historical Notes Exercises 201 References 201 AUTHOR INDEX 204 SUBJECT INDEX 210

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