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

Series: Chapman & Hall/CRC Monographs on Statistics & Applied Probability (Book 57). — Chapman and Hall/CRC, 1993. — 436 p. — ISBN: 978-0412042317, e-ISBN: 978-1489945419.Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach in An Introduction to the Bootstrap avoids that wall. It arms scientists and engineers, as well as statisticians, with the computational techniques they need to analyze and understand complicated data sets.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.