The Jackknife and Bootstrap

1. Front Matter

   Pages i-xvii

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2. Introduction

   • Jun Shao, Dongsheng Tu

   Pages 1-22

3. Theory for the Jackknife

   • Jun Shao, Dongsheng Tu

   Pages 23-70

4. Theory for the Bootstrap

   • Jun Shao, Dongsheng Tu

   Pages 71-128

5. Bootstrap Confidence Sets and Hypothesis Tests

   • Jun Shao, Dongsheng Tu

   Pages 129-189

6. Computational Methods

   • Jun Shao, Dongsheng Tu

   Pages 190-231

7. Applications to Sample Surveys

   • Jun Shao, Dongsheng Tu

   Pages 232-282

8. Applications to Linear Models

   • Jun Shao, Dongsheng Tu

   Pages 283-330

9. Applications to Nonlinear, Nonparametric, and Multivariate Models

   • Jun Shao, Dongsheng Tu

   Pages 331-385

10. Applications to Time Series and Other Dependent Data

    • Jun Shao, Dongsheng Tu

    Pages 386-415

11. Bayesian Bootstrap and Random Weighting

    • Jun Shao, Dongsheng Tu

    Pages 416-446

12. Back Matter

    Pages 447-517

    PDF

The jackknife and bootstrap are the most popular data-resampling meth­ ods used in statistical analysis. The resampling methods replace theoreti­ cal derivations required in applying traditional methods (such as substitu­ tion and linearization) in statistical analysis by repeatedly resampling the original data and making inferences from the resamples. Because of the availability of inexpensive and fast computing, these computer-intensive methods have caught on very rapidly in recent years and are particularly appreciated by applied statisticians. The primary aims of this book are (1) to provide a systematic introduction to the theory of the jackknife, the bootstrap, and other resampling methods developed in the last twenty years; (2) to provide a guide for applied statisticians: practitioners often use (or misuse) the resampling methods in situations where no theoretical confirmation has been made; and (3) to stimulate the use of the jackknife and bootstrap and further devel­ opments of the resampling methods. The theoretical properties of the jackknife and bootstrap methods are studied in this book in an asymptotic framework. Theorems are illustrated by examples. Finite sample properties of the jackknife and bootstrap are mostly investigated by examples and/or empirical simulation studies. In addition to the theory for the jackknife and bootstrap methods in problems with independent and identically distributed (Li.d.) data, we try to cover, as much as we can, the applications of the jackknife and bootstrap in various complicated non-Li.d. data problems.

• Bootstrapping
• Covariance matrix
• Estimator
• Factor analysis
• Generalized linear model
• Likelihood
• Monte Carlo method
• Resampling
• STATISTICA
• Time series
• Uniform integrability
• Variance
• linear regression
• mathematical statistics
• statistics

• Department of Statistics, University of Wisconsin, Madison, Madison, USA

  Jun Shao

• Institute of System Science, Academia Sinica, Beijing, People’s Republic of China

  Dongsheng Tu