The Jackknife and Bootstrap

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-Esséen Theorem. - A. 10 Edgeworth Expansions. - A. 11 Cornish-Fisher Expansions. - Appendix B. Notation. - References. - Author Index. Language: English