The Jackknife and Bootstrap - Dongsheng Tu

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Biographie:
Jun Shao is Professor of Statistics at the University of Wisconsin, Madison....

Sommaire:
1. Introduction.- 1.1 Statistics and Their Sampling Distributions.- 1.2 The Traditional Approach.- 1.3 The Jackknife.- 1.4 The Bootstrap.- 1.5 Extensions to Complex Problems.- 1.6 Scope of Our Studies.- 2. Theory for the Jackknife.- 2.1 Variance Estimation for Functions of Means.- 2.2 Variance Estimation for Functionals.- 2.3 The Delete-d Jackknife.- 2.4 Other Applications.- 2.5 Conclusions and Discussions.- 3. Theory for the Bootstrap.- 3.1 Techniques in Proving Consistency.- 3.2 Consistency: Some Major Results.- 3.3 Accuracy and Asymptotic Comparisons.- 3.4 Fixed Sample Performance.- 3.5 Smoothed Bootstrap.- 3.6 Nonregular Cases.- 3.7 Conclusions and Discussions.- 4. Bootstrap Confidence Sets and Hypothesis Tests.- 4.1 Bootstrap Confidence Sets.- 4.2 Asymptotic Theory.- 4.3 The Iterative Bootstrap and Other Methods.- 4.4 Empirical Comparisons.- 4.5 Bootstrap Hypothesis Tests.- 4.6 Conclusions and Discussions.- 5. Computational Methods.- 5.1 The Delete-1 Jackknife.- 5.2 The Delete-d Jackknife.- 5.3 Analytic Approaches for the Bootstrap.- 5.4 Simulation Approaches for the Bootstrap.- 5.5 Conclusions and Discussions.- 6. Applications to Sample Surveys.- 6.1 Sampling Designs and Estimates.- 6.2 Resampling Methods.- 6.3 Comparisons by Simulation.- 6.4 Asymptotic Results.- 6.5 Resampling Under Imputation.- 6.6 Conclusions and Discussions.- 7. Applications to Linear Models.- 7.1 Linear Models and Regression Estimates.- 7.2 Variance and Bias Estimation.- 7.3 Inference and Prediction Using the Bootstrap.- 7.4 Model Selection.- 7.5 Asymptotic Theory.- 7.6 Conclusions and Discussions.- 8. Applications to Nonlinear, Nonparametric, and Multivariate Models.- 8.1 Nonlinear Regression.- 8.2 Generalized Linear Models.- 8.3 Cox's Regression Models.- 8.4 Kernel Density Estimation.-8.5 Nonparametric Regression.- 8.6 Multivariate Analysis.- 8.7 Conclusions and Discussions.- 9. Applications to Time Series and Other Dependent Data.- 9.1 m-Dependent Data.- 9.2 Markov Chains.- 9.3 Autoregressive Time Series.- 9.4 Other Time Series.- 9.5 Stationary Processes.- 9.6 Conclusions and Discussions.- 10. Bayesian Bootstrap and Random Weighting.- 10.1 Bayesian Bootstrap.- 10.2 Random Weighting.- 10.3 Random Weighting for Functional and Linear Models.- 10.4 Empirical Results for Random Weighting.- 10.5 Conclusions and Discussions.- Appendix A. Asymptotic Results.- A.1 Modes of Convergence.- A.2 Convergence of Transformations.- A.4 The Borel-Cantelli Lemma.- A.5 The Law of Large Numbers.- A.6 The Law of the Iterated Logarithm.- A.7 Uniform Integrability.- A.8 The Central Limit Theorem.- A.9 The Berry-Ess?en Theorem.- A.10 Edgeworth Expansions.- A.11 Cornish-Fisher Expansions.- Appendix B. Notation.- References.- Author Index.