An Introduction to the BootstrapAn Introduction to the Bootstrap arms scientists and engineers as well as 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. |
Contents
| 1 | |
| 10 | |
3 Random samples and probabilities | 17 |
4 The empirical distribution function and the plugin principle | 31 |
5 Standard errors and estimated standard errors | 39 |
6 The bootstrap estimate of standard error | 45 |
some examples | 60 |
8 More complicated data structures | 86 |
17 Crossvalidation and other estimates of prediction error | 237 |
18 Adaptive estimation and calibration | 258 |
19 Assessing the error in bootstrap estimates | 271 |
20 A geometrical representation for the bootstrap and jackknife | 283 |
21 An overview of nonparametric and parametric inference | 296 |
22 Further topics in bootstrap confidence intervals | 321 |
23 Efficient bootstrap computations | 338 |
24 Approximate likelihoods | 358 |
9 Regression models | 105 |
10 Estimates of bias | 124 |
11 The jackknife | 141 |
12 Confidence intervals based on bootstrap tables | 153 |
13 Confidence intervals based on bootstrap percentiles | 168 |
14 Better bootstrap confidence intervals | 178 |
15 Permutation tests | 202 |
16 Hypothesis testing with the bootstrap | 220 |
25 Bootstrap bioequivalence | 372 |
26 Discussion and further topics | 392 |
software for bootstrap computations | 398 |
| 413 | |
Author index | 426 |
| 430 | |
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Common terms and phrases
ABC intervals algorithm approximation ASLperm BCa interval bioequivalence boot bootstrap computations bootstrap confidence intervals bootstrap data set bootstrap replications bootstrap samples bootstrap-t calculations calibration Chapter components compute confidence intervals confidence point cross-validation curve data points defined delta method density discussed distribution F distribution function Efron empirical distribution empirical distribution function endpoints equal estimate bias estimate of bias estimate of standard estimate of variance example exponential family Fisher information formula gives histogram hormone data hypothesis test infinitesimal jackknife jackknife estimate least-squares left panel linear LSAT matrix maximum likelihood median mouse data nonparametric normal distribution normal theory null hypothesis number of bootstrap observed obtained panel of Figure parameter parametric bootstrap percentile interval permutation test plug-in estimate population prediction error probability distribution problem quadratic random sample random variable regression resampling right panel shows standard deviation standard error standard normal strap Suppose Table theta tion vector