The jackknife and bootstrap

摘要: 1. Introduction.- 1.1 Statistics and Their Sampling Distributions.- 1.2 The Traditional Approach.- 1.3 Jackknife.- 1.4 Bootstrap.- 1.5 Extensions to Complex Problems.- 1.6 Scope of Our Studies.- 2. Theory for the 2.1 Variance Estimation Functions Means.- 2.1.1 Consistency.- 2.1.2 Other properties.- 2.1.3 Discussions examples.- 2.2 Functionals.- 2.2.1 Differentiability consistency.- 2.2.2 Examples.- 2.2.3 Convergence rate.- 2.2.4 differential approaches.- 2.3 Delete-d 2.3.1 estimation.- 2.3.2 Jackknife histograms.- 2.4 Applications.- 2.4.1 Bias 2.4.2 reduction.- 2.4.3 Miscellaneous results.- 2.5 Conclusions Discussions.- 3. 3.1 Techniques in Proving 3.1.1 Bootstrap distribution estimators.- 3.1.2 Mallows' distance.- 3.1.3 Berry-Esseen's inequality.- 3.1.4 Imitation.- 3.1.5 Linearization.- 3.1.6 moments.- 3.2 Consistency: Some Major Results.- 3.2.1 Distribution 3.2.2 3.3 Accuracy Asymptotic Comparisons.- 3.3.1 3.3.2 minimaxity.- 3.3.3 mean squared error.- 3.3.4 relative 3.3.5 Conclusions.- 3.4 Fixed Sample Performance.- 3.4.1 Moment 3.4.2 3.4.3 3.5 Smoothed 3.5.1 Empirical evidences 3.5.2 quantiles.- 3.5.3 Remarks.- 3.6 Nonregular Cases.- 3.7 4. Confidence Sets Hypothesis Tests.- 4.1 Sets.- 4.1.1 bootstrap-t.- 4.1.2 bootstrap percentile.- 4.1.3 bias-corrected 4.1.4 accelerated 4.1.5 hybrid bootstrap.- 4.2 Theory.- 4.2.1 4.2.2 Accuracy.- 4.2.3 asymptotic comparisons.- 4.3 Iterative Methods.- 4.3.1 iterative 4.3.2 calibrating.- 4.3.3 automatic percentile variance stabilizing.- 4.3.4 width confidence intervals.- 4.3.5 Likelihood based sets.- 4.4 4.4.1 bootstrap-t, percentile, BC, BCa.- 4.4.2 other methods.- 4.4.3 calibration.- 4.4.4 Summary.- 4.5 4.5.1 General description.- 4.5.2 Two-sided hypotheses with nuisance parameters.- 4.5.3 distance tests.- 4.5.4 results discussions.- 4.6 5. Computational 5.1 Delete-1 5.1.1 one-step jackknife.- 5.1.2 Grouping random subsampling.- 5.2 5.2.1 Balanced 5.2.2 Random 5.3 Analytic Approaches 5.3.1 delta method.- 5.3.2 approximations.- 5.3.3 Saddle point 5.3.4 5.4 Simulation 5.4.1 simple Monte Carlo 5.4.2 resampling.- 5.4.3 Centering after Carlo.- 5.4.4 linear 5.4.5 Antithetic 5.4.6 Importance 5.4.7 5.5 6. Applications Surveys.- 6.1 Designs Estimates.- 6.2 Resampling 6.2.1 6.2.2 balanced repeated replication.- 6.2.3 Approximated BRR 6.2.4 6.3 Comparisons by Simulation.- 6.4 6.4.1 Assumptions.- 6.4.2 jackknife functions averages.- 6.4.3 RGBRR RSBRR 6.4.4 6.4.5 sample 6.5 Under Imputation.- 6.5.1 Hot deck imputation.- 6.5.2 An adjusted 6.5.3 Multiple hot 6.5.4 Bootstrapping under 6.6 7. Linear Models.- 7.1 Models Regression 7.2 Estimation.- 7.2.1 Weighted unweighted jackknives.- 7.2.2 Three types bootstraps.- 7.2.3 Robustness efficiency.- 7.3 Inference Prediction Using 7.3.1 7.3.2 Simultaneous 7.3.3 7.3.4 Prediction.- 7.4 Model Selection.- 7.4.1 Cross-validation.- 7.4.2 7.5 7.5.1 7.5.2 7.5.3 7.5.4 prediction.- 7.5.5 selection.- 7.6 8. Nonlinear, Nonparametric, Multivariate 8.1 Nonlinear Regression.- 8.1.1 8.1.2 distributions 8.1.3 Cross-validation model 8.2 Generalized 8.2.1 8.2.2 procedures.- 8.2.3 selection bootstrapping.- 8.3 Cox's 8.3.1 8.3.2 8.4 Kernel Density 8.4.1 Bandwidth cross-validation.- 8.4.2 8.4.3 8.5 Nonparametric 8.5.1 estimates fixed design.- 8.5.2 regressor.- 8.5.3 Nearest neighbor estimates.- 8.5.4 Smoothing splines.- 8.6 Analysis.- 8.6.1 Analysis covariance matrix.- 8.6.2 models.- 8.6.3 Discriminant analysis.- 8.6.4 Factor analysis clustering.- 8.7 9. Time Series Dependent Data.- 9.1 m-Dependent 9.2 Markov Chains.- 9.3 Autoregressive Series.- 9.3.1 residuals.- 9.3.2 9.4 9.4.1 ARMA(p,q) 9.4.2 regression time series errors.- 9.4.3 Dynamical regression.- 9.5 Stationary Processes.- 9.5.1 Moving block circular block.- 9.5.2 Consistency 9.5.3 9.5.4 9.6 10. Bayesian Weighting.- 10.1 10.1.1 a noninformative prior.- 10.1.2 using prior information.- 10.1.3 weighted likelihood 10.1.4 remarks.- 10.2 10.2.1 Motivation.- 10.2.2 10.2.3 accuracy.- 10.3 Weighting Functional 10.3.1 Statistical functionals.- 10.3.2 10.4 Results 10.5 Appendix A. A.1 Modes Convergence.- A.2 Transformations.- A.4 Borel-Cantelli Lemma.- A.5 Law Large Numbers.- A.6 Iterated Logarithm.- A.7 Uniform Integrability.- A.8 Central Limit Theorem.- A.9 Berry-Esseen A.10 Edgeworth Expansions.- A.11 Cornish-Fisher B. Notation.- References.- Author Index.