Efron B., Tibshirani R.J. An Introduction to the Bootstrap

Chapman and Hall/CRC, 1993. — 436 p. — (Chapman & Hall/CRC Monographs on Statistics & Applied Probability 57). — ISBN10: 0412042312
ISBN13: 978-0412042317.The bootstrap is a computer-based method of statistical inference that can answer many real statistical questions without formulas. The goal of this book is to arm scientists and engineers, as well as statisticians, with computational techniques that they can use to analyze and understand complicated data sets. The book describes the bootstrap and other methods for assessing statistical accuracy. The bootstrap does not work in isolation but rather is applied to a wide variety of statistical procedures. Part of the objective of this book is expose the reader to many exciting and useful statistical techniques through real-data examples. Some of the techniques described include nonparametric regression, density estimation, classification trees, and least median of squares regression.
Much of the exposition in the book is based on the analysis of real data sets. The mouse data, the stamp data, the tooth data, the hormone data, and other small but genuine examples, are an important part of the presentation. These are especially valuable if the reader can try his own computations on them.
This book does not give a rigorous technical treatment of the bootstrap, and it concentrates on the ideas rather than their mathematical justification. Many of these ideas are quite sophisticated, however, and this book is not just for beginners. The presentation starts off slowly but builds in both its scope and depth. More mathematically advanced accounts of the bootstrap may be found in papers and books by many researchers that are listed in the Bibliographic notes at the end of the chapters.The accuracy of a sample mean
Random samples and probabilities
The empirical distribution function and the plug-in principle
Standard errors and estimated standard errors
The bootstrap estimate of standard error
Bootstrap standard errors: some examples
More complicated data structures
Regression models
Estimates of bias
The jackknife
Confidence intervals based on bootstrap "tables"
Confidence intervals based on bootstrap percentiles
Better bootstrap confidence intervals
Permutation tests
Hypothesis testing with the bootstrap
Cross-validation and other estimates of prediction error
Adaptive estimation and calibration
Assessing the error in bootstrap estimates
A geometrical representation for the bootstrap and jackknife
An overview of nonparametric and parametric inference
Further topics in bootstrap confidence intervals
Efficient bootstrap computations
Approximate likelihoods
Bootstrap bioequivalence
Discussion and further topics
Appendix: software for bootstrap computations