Davison A.C., Hinkley D.V. Bootstrap Methods and their Application

Cambridge University Press, 1997. — 594 p. — ISBN: 0521574714, 978-0521574716.This book gives a broad and up-to-date coverage of bootstrap methods, with numerous applied examples, developed in a coherent way with the necessary theoretical basis. Applications include stratified data; finite populations; censored and missing data; linear, nonlinear, and smooth regression models; classification; time series and spatial problems. Special features of the book include: extensive discussion of significance tests and confidence intervals; material on various diagnostic methods; and methods for efficient computation, including improved Monte Carlo simulation. Each chapter includes both practical and theoretical exercises.The Basic Bootstraps.
Parametric Simulation, Nonparametric Simulation, Simple Confidence Intervals, Reducing Error,
Statistical Issues, Nonparametric Approximations for Variance and Bias, Subsampling Methods.
Further Ideas.
Several Samples, Semiparametric Models, Smooth Estimates of F, Censoring, Missing Data,
Finite Population Sampling, Hierarchical Data, Bootstrapping the Bootstrap,
Bootstrap Diagnostics, Choice of Estimator from the Data.
Tests.
Resampling for Parametric Tests, Nonparametric Permutation Tests, Nonparametric Bootstrap Tests,
Adjusted P-values, Estimating Properties of Tests.
Confidence Intervals.
Basic Confidence Limit Methods, Percentile Methods, Theoretical Comparison of Methods,
Inversion of Significance Tests, Double Bootstrap Methods,
Empirical Comparison of Bootstrap Methods, Multiparameter Methods,
Conditional Confidence Regions, Prediction.
Linear Regression.
Least Squares Linear Regression, Multiple Linear Regression, Aggregate Prediction Error and Variable Selection, Robust Regression.
Further Topics in Regression.
Generalized Linear Models, Survival Data, Other Nonlinear Models, Misclassification Error, Nonparametric Regression.
Complex Dependence.
Introduction, Time Series, Point Processes.
Improved Calculation.
Balanced Bootstraps, Control Methods, Importance Resampling, Saddlepoint Approximation.
Semiparametric Likelihood Inference.
Likelihood, Multinomial-Based Likelihoods, Bootstrap Likelihood, Likelihood Based on Confidence Sets, Bayesian Bootstraps.
Computer Implementation.
Bootstraps, Further Ideas, Tests, Confidence Intervals, Linear Regression, Further Topics in Regression,
Time Series, Improved Simulation, Semiparametric Likelihoods.
Appendix A. Cumulant Calculations.