An Introduction to Bootstrap Methods with Applications to R

CONTENTS

PREFACE

ACKNOWLEDGMENTS

LIST OF TABLES

1 INTRODUCTION

1.1 Historical Background

1.2 Definition and Relationship to the Delta Method and Other Resampling Methods

1.2.1 Jackknife

1.2.2 Delta Method

1.2.3 Cross-Validation

1.2.4 Subsampling

1.3 Wide Range of Applications

1.4 The Bootstrap and the R Language System

1.5 Historical Notes

1.6 Exercises

References

2 ESTIMATION

2.1 Estimating Bias

2.1.1 Bootstrap Adjustment

2.1.2 Error Rate Estimation in Discriminant Analysis

2.1.3 Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation

2.1.4 Patch Data Example

2.2 Estimating Location

2.2.1 Estimating a Mean

2.2.2 Estimating a Median

2.3 Estimating Dispersion

2.3.1 Estimating an Estimate's Standard Error

2.3.2 Estimating Interquartile Range

2.4 Linear Regression

2.4.1 Overview

2.4.2 Bootstrapping Residuals

2.4.3 Bootstrapping Pairs (Response and Predictor Vector)

2.4.4 Heteroscedasticity of Variance: The Wild Bootstrap

2.4.5 A Special Class of Linear Regression Models: Multivariable Fractional Polynomials

2.5 Nonlinear Regression

2.5.1 Examples of Nonlinear Models

2.5.2 A Quasi-Optical Experiment

2.6 Nonparametric Regression

2.6.1 Examples of Nonparametric Regression Models

2.6.2 Bootstrap Bagging

2.7 Historical Notes

2.8 Exercises

References

3 CONFIDENCE INTERVALS

3.1 Subsampling, Typical Value Theorem, and Efron's Percentile Method

3.2 Bootstrap-t

3.3 Iterated Bootstrap

3.4 Bias-Corrected (BC) Bootstrap

3.5 BCa and ABC

3.6 Tilted Bootstrap

3.7 Variance Estimation ...