An Introduction to the Bootstrap 1st Edition by Bradley Efron, Tibshirani ISBN 1040080014 9781040080016

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ISBN 10: 1040080014
ISBN 13: 9781040080016
Author: Bradley Efron, R.J. Tibshirani

An Introduction to the Bootstrap arms scientists and engineers as well as statisticians with the computational techniques they need to analyze and understand complicated data sets. The bootstrap is a computer-based method of statistical inference that answers statistical questions without formulas and gives a direct appreciation of variance, bias, coverage, and other probabilistic phenomena. This book presents an overview of the bootstrap and related methods for assessing statistical accuracy, concentrating on the ideas rather than their mathematical justification. Not just for beginners, the presentation starts off slowly, but builds in both scope and depth to ideas that are quite sophisticated.

An Introduction to the Bootstrap 1st Table of contents:

1 Introduction

1.1 An overview of this book

1.2 Information for instructors

1.3 Some of the notation used in the book

2 The accuracy of a sample mean

2.1 Problems

3 Random samples and probabilities

3.1 Introduction

3.2 Random samples

3.3 Probability theory

3.4 Problems

4 The empirical distribution function and the plug-in principle

4.1 Introduction

4.2 The empirical distribution function

4.3 The plug-in principle

4.4 Problems

5 Standard errors and estimated standard errors

5.1 Introduction

5.2 The standard error of a mean

5.3 Estimating the standard error of the mean

5.4 Problems

6 The bootstrap estimate of standard error

6.1 Introduction

6.2 The bootstrap estimate of standard error

6.3 Example: the correlation coefficient

6.4 The number of bootstrap replications B

6.5 The parametric bootstrap

6.6 Bibliographic notes

6.7 Problems

7 Bootstrap standard errors: some examples

7.1 Introduction

7.2 Example 1: test score data

7.3 Example 2: curve fitting

7.4 An example of bootstrap failure

7.5 Bibliographic notes

7.6 Problems

8 More complicated data structures

8.1 Introduction

8.2 One-sample problems

8.3 The two-sample problem

8.4 More general data structures

8.5 Example: lutenizing hormone

8.6 The moving blocks bootstrap

8.7 Bibliographic notes

8.8 Problems

9 Regression models

9.1 Introduction

9.2 The linear regression model

9.3 Example: the hormone data

9.4 Application of the bootstrap

9.5 Bootstrapping pairs vs bootstrapping residuals

9.6 Example: the cell survival data

9.7 Least median of squares

9.8 Bibliographic notes

9.9 Problems

10 Estimates of bias

10.1 Introduction

10.2 The bootstrap estimate of bias

10.3 Example: the patch data

10.4 An improved estimate of bias

10.5 The jackknife estimate of bias

10.6 Bias correction

10.7 Bibliographic notes

10.8 Problems

11 The jackknife

11.1 Introduction

11.2 Definition of the jackknife

11.3 Example: test score data

11.4 Pseudo-values

11.5 Relationship between the jackknife and bootstrap

11.6 Failure of the jackknife

11.7 The delete-d jackknife

11.8 Bibliographic notes

11.9 Problems

12 Confidence intervals based on bootstrap “tables”

12.1 Introduction

12.2 Some background on confidence intervals

12.3 Relation between confidence intervals and hypothesis tests

12.4 Student’s t interval

12.5 The bootstrap-t interval

12.6 Transformations and the bootstrap-t

12.7 Bibliographic notes

12.8 Problems

13 Confidence intervals based on bootstrap percentiles

13.1 Introduction

13.2 Standard normal intervals

13.3 The percentile interval

13.4 Is the percentile interval backwards?

13.5 Coverage performance

13.6 The transformation-respecting property

13.7 The range-preserving property

13.8 Discussion

13.9 Bibliographic notes

13.10 Problems

14 Better bootstrap confidence intervals

14.1 Introduction

14.2 Example: the spatial test data

14.3 The BCa method

14.4 The ABC method

14.5 Example: the tooth data

14.6 Bibliographic notes

14.7 Problems

15 Permutation tests

15.1 Introduction

15.2 The two-sample problem

15.3 Other test statistics

15.4 Relationship of hypothesis tests to confidence intervals and the bootstrap

15.5 Bibliographic notes

15.6 Problems

16 Hypothesis testing with the bootstrap

16.1 Introduction

16.2 The two-sample problem

16.3 Relationship between the permutation test and the bootstrap

16.4 The one-sample problem

16.5 Testing multimodality of a population

16.6 Discussion

16.7 Bibliographic notes

16.8 Problems

17 Cross-validation and other estimates of predictior error

17.1 Introduction

17.2 Example: hormone data

17.3 Cross-validation

17.4 Cp and other estimates of prediction error

17.5 Example: classification trees

17.6 Bootstrap estimates of prediction error

17.6.1 Overview

17.6.2 Some details

17.7 The .632 bootstrap estimator

17.8 Discussion

17.9 Bibliographic notes

17.10 Problems

18 Adaptive estimation and calibration

18.1 Introduction

18.2 Example: smoothing parameter selection for curve fitting

18.3 Example: calibration of a confidence point

18.4 Some general considerations

18.5 Bibliographic notes

18.6 Problems

19 Assessing the error in bootstrap estimates

19.1 Introduction

19.2 Standard error estimation

19.3 Percentile estimation

19.4 The jackknife-after-bootstrap

19.5 Derivations

19.6 Bibliographic notes

19.7 Problems

20 A geometrical representation for the bootstrap and jackknife

20.1 Introduction

20.2 Bootstrap sampling

20.3 The jackknife as an approximation to the bootstrap

20.4 Other jackknife approximations

20.5 Estimates of bias

20.6 An example

20.7 Bibliographic notes

20.8 Problems

21 An overview of nonparametric and parametric inference

21.1 Introduction

21.2 Distributions, densities and likelihood functions

21.3 Functional statistics and influence functions

21.4 Parametric maximum likelihood inference

21.5 The parametric bootstrap

21.6 Relation of parametric maximum likelihood, bootstrap and jackknife approaches

21.6.1 Example: influence components for the mean

21.7 The empirical cdf as a maximum likelihood estimate

21.8 The sandwich estimator

21.8.1 Example: Mouse data

21.9 The delta method

21.9.1 Example: delta method for the mean

21.9.2 Example: delta method for the correlation coefficient

21.10 Relationship between the delta method and infinitesimal jackknife

21.11 Exponential families

21.12 Bibliographic notes

21.13 Problems

22 Further topics in bootstrap confidence intervals

22.1 Introduction

22.2 Correctness and accuracy

22.3 Confidence points based on approximate pivots

22.4 The BCa interval

22.5 The underlying basis for the BCa interval

22.6 The ABC approximation

22.7 Least favorable families

22.8 The ABCq method and transformations

22.9 Discussion

22.10 Bibliographic notes

22.11 Problems

23 Efficient bootstrap computations

23.1 Introduction

23.2 Post-sampling adjustments

23.3 Application to bootstrap bias estimation

23.4 Application to bootstrap variance estimation

23.5 Pre- and post-sampling adjustments

23.6 Importance sampling for tail probabilities

23.7 Application to bootstrap tail probabilities

23.8 Bibliographic notes

23.9 Problems

24 Approximate likelihoods

24.1 Introduction

24.2 Empirical likelihood

24.3 Approximate pivot methods

24.4 Bootstrap partial likelihood

24.5 Implied likelihood

24.6 Discussion

24.7 Bibliographic notes

24.8 Problems

25 Bootstrap bioequivalence

25.1 Introduction

25.2 A bioequivalence problem

25.3 Bootstrap confidence intervals

25.4 Bootstrap power calculations

25.5 A more careful power calculation

25.6 Fieller’s intervals

25.7 Bibliographic notes

25.8 Problems

26 Discussion and further topics

26.1 Discussion

26.2 Some questions about the bootstrap

26.3 References on further topics

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