An Introduction to the Bootstrap

An Introduction to the Bootstrap arms scientists, engineers, and statisticians with the computational techniques they need to analyze and understand complicated data sets. The bootstrap is a computer-based method of statistical inference that answers statistical questions without formulas and gives a direct appreciation of variance, bias, coverage, and other probabilistic phenomena. This book presents an overview of the bootstrap and related methods for assessing statistical accuracy, concentrating on the ideas rather than their mathematical justification. Not just for beginners, the presentation starts off slowly, but builds in both scope and depth to ideas that are quite sophisticated.

Preface 1 Introduction 3 -Random samples and probabilities 4 The empirical distribution function and the plug-in principle 5 Standard errors and estimated standard errors 6 The bootstrap estimate of standard error 7 Bootstrap standard errors: some examples 8 More complicated data structures 9 Regression models 10 Estimates of bias 11 The jackknife 12 Confidence intervals based on bootstrap "tables" 13 Confidence intervals based on bootstrap percentiles 14 Better bootstrap confidence intervals 15 Permutation tests 16 Hypothesis testing with the bootstrap 17 Cross-validation and other estimates of prediction error 18 Adaptive estimation and calibration 19 Assessing the error in bootstrap estimates 20 A geometrical representation for the bootstrap and jackknife 21 An overview of nonparametric and parametric Inference 22 Further topics in bootstrap confidence intervals 23 Efficient bootstrap computations 24 Approximate likelihoods 25 Bootstrap bioequivalence 26 Discussion and further topics