Introduction to Bootstrap Methods with Applications to R

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 xiAcknowledgments xvList of Tables xvii1 Introduction 11.1 Historical Background 11.2 Definition and Relationship to the Delta Method and Other Resampling Methods 31.2.1 Jackknife 61.2.2 Delta Method 71.2.3 Cross-Validation 71.2.4 Subsampling 81.3 Wide Range of Applications 81.4 The Bootstrap and the R Language System 101.5 Historical Notes 251.6 Exercises 26References 272 Estimation 302.1 Estimating Bias 302.1.1 Bootstrap Adjustment 302.1.2 Error Rate Estimation in Discriminant Analysis 322.1.3 Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation 422.1.4 Patch Data Example 512.2 Estimating Location 532.2.1 Estimating a Mean 532.2.2 Estimating a Median 542.3 Estimating Dispersion 542.3.1 Estimating an Estimate’s Standard Error 552.3.2 Estimating Interquartile Range 562.4 Linear Regression 562.4.1 Overview 562.4.2 Bootstrapping Residuals 572.4.3 Bootstrapping Pairs (Response and Predictor Vector) 582.4.4 Heteroscedasticity of Variance: The Wild Bootstrap 582.4.5 A Special Class of Linear Regression Models: Multivariable Fractional Polynomials 602.5 Nonlinear Regression 602.5.1 Examples of Nonlinear Models 612.5.2 A Quasi-Optical Experiment 632.6 Nonparametric Regression 632.6.1 Examples of Nonparametric Regression Models 642.6.2 Bootstrap Bagging 662.7 Historical Notes 672.8 Exercises 69References 713 Confidence Intervals 763.1 Subsampling, Typical Value Theorem, and Efron’s Percentile Method 773.2 Bootstrap-t 793.3 Iterated Bootstrap 833.4 Bias-Corrected (BC) Bootstrap 853.5 BCa and ABC 853.6 Tilted Bootstrap 883.7 Variance Estimation with Small Sample Sizes 903.8 Historical Notes 943.9 Exercises 96References 984 Hypothesis Testing 1014.1 Relationship to Confidence Intervals 1034.2 Why Test Hypotheses Differently? 1054.3 Tendril DX Example 1064.4 Klingenberg Example: Binary Dose–Response 1084.5 Historical Notes 1094.6 Exercises 110References 1115 Time Series 1135.1 Forecasting Methods 1135.2 Time Domain Models 1145.3 Can Bootstrapping Improve Prediction Intervals? 1155.4 Model-Based Methods 1185.4.1 Bootstrapping Stationary Autoregressive Processes 1185.4.2 Bootstrapping Explosive Autoregressive Processes 1235.4.3 Bootstrapping Unstable Autoregressive Processes 1235.4.4 Bootstrapping Stationary ARMA Processes 1235.5 Block Bootstrapping for Stationary Time Series 1235.6 Dependent Wild Bootstrap (DWB) 1265.7 Frequency-Based Approaches for Stationary Time Series 1275.8 Sieve Bootstrap 1285.9 Historical Notes 1295.10 Exercises 131References 1316 Bootstrap Variants 1366.1 Bayesian Bootstrap 1376.2 Smoothed Bootstrap 1386.3 Parametric Bootstrap 1396.4 Double Bootstrap 1396.5 The m-Out-of-n Bootstrap 1406.6 The Wild Bootstrap 1416.7 Historical Notes 1416.8 Exercises 142References 1427 Chapter Special Topics 1447.1 Spatial Data 1447.1.1 Kriging 1447.1.2 Asymptotics for Spatial Data 1477.1.3 Block Bootstrap on Regular Grids 1487.1.4 Block Bootstrap on Irregular Grids 1487.2 Subset Selection in Regression 1487.2.1 Gong’s Logistic Regression Example 1497.2.2 Gunter’s Qualitative Interaction Example 1537.3 Determining the Number of Distributions in a Mixture 1557.4 Censored Data 1577.5 P-Value Adjustment 1587.5.1 The Westfall–Young Approach 1597.5.2 Passive Plus Example 1597.5.3 Consulting Example 1607.6 Bioequivalence 1627.6.1 Individual Bioequivalence 1627.6.2 Population Bioequivalence 1657.7 Process Capability Indices 1657.8 Missing Data 1727.9 Point Processes 1747.10 Bootstrap to Detect Outliers 1767.11 Lattice Variables 1777.12 Covariate Adjustment of Area Under the Curve Estimates for Receiver Operating Characteristic (ROC) Curves 1777.13 Bootstrapping in SAS 1797.14 Historical Notes 1827.15 Exercises 183References 1858 When the Bootstrap is Inconsistent and How to Remedy it 1908.1 Too Small of a Sample Size 1918.2 Distributions with Infinite Second Moments 1918.2.1 Introduction 1918.2.2 Example of Inconsistency 1928.2.3 Remedies 1938.3 Estimating Extreme Values 1948.3.1 Introduction 1948.3.2 Example of Inconsistency 1948.3.3 Remedies 1948.4 Survey Sampling 1958.4.1 Introduction 1958.4.2 Example of Inconsistency 1958.4.3 Remedies 1958.5 m-Dependent Sequences 1968.5.1 Introduction 1968.5.2 Example of Inconsistency When Independence Is Assumed 1968.5.3 Remedy 1978.6 Unstable Autoregressive Processes 1978.6.1 Introduction 1978.6.2 Example of Inconsistency 1978.6.3 Remedies 1978.7 Long-Range Dependence 1988.7.1 Introduction 1988.7.2 Example of Inconsistency 1988.7.3 A Remedy 1988.8 Bootstrap Diagnostics 1998.9 Historical Notes 1998.10 Exercises 201References 201Author Index 204Subject Index 210

“I recommend this text to anyone wishing to apply computationally intensive methods and if you only purchase one book on bootstrap methods then this could be the book for you!.”  (International Statistical Review, 2012)