Bootstrap Methods: With Applications in R

Preface
Acknowledgements
Contents
Abbreviations
1 Introduction
	1.1 Basic Idea of the Bootstrap
	1.2 The R-Project for Statistical Computing
	1.3 Usage of R in This Book
		1.3.1 Further Non-Statistical R-Packages
	References
2 Generating Random Numbers
	2.1 Distributions in the R-Package Stats
	2.2 Uniform df. on the Unit Interval
	2.3 The Quantile Transformation
	2.4 The Normal Distribution
	2.5 Method of Rejection
	2.6 Generation of Random Vectors
	2.7 Exercises
	References
3 The Classical Bootstrap
	3.1 An Introductory Example
	3.2 Basic Mathematical Background of the Classical Bootstrap
	3.3 Discussion of the Asymptotic Accuracy of the Classical Bootstrap
	3.4 Empirical Process and the Classical Bootstrap
	3.5 Mathematical Framework of Mallow's Metric
	3.6 Exercises
	References
4 Bootstrap-Based Tests
	4.1 Introduction
	4.2 The One-Sample Test
	4.3 Two-Sample Tests
	4.4 Goodness-of-Fit (GOF) Test
	4.5 Mathematical Framework of the GOF Test
	4.6 Exercises
	References
5 Regression Analysis
	5.1 Homoscedastic Linear Regression under Fixed Design
		5.1.1 Model-Based Bootstrap
		5.1.2 LSE Asymptotic
		5.1.3 LSE Bootstrap Asymptotic
	5.2 Linear Correlation Model and the Bootstrap
		5.2.1 Classical Bootstrap
		5.2.2 Wild Bootstrap
		5.2.3 Mathematical Framework of LSE
		5.2.4 Mathematical Framework of Classical Bootstrapped LSE
		5.2.5 Mathematical Framework of Wild Bootstrapped LSE
	5.3 Generalized Linear Model (Parametric)
		5.3.1 Mathematical Framework of MLE
		5.3.2 Mathematical Framework of Bootstrap MLE
	5.4 Semi-parametric Model
		5.4.1 Mathematical Framework of LSE
		5.4.2 Mathematical Framework of Wild Bootstrap LSE
	5.5 Exercises
	References
6 Goodness-of-Fit Test for Generalized Linear Models
	6.1 MEP in the Parametric Modeling Context
		6.1.1 Implementation
		6.1.2 Bike Sharing Data
		6.1.3 Artificial Data
	6.2 MEP in the Semi-parametric Modeling Context
		6.2.1 Implementation
		6.2.2 Artificial Data
	6.3 Comparison of the GOF Tests under the Parametric and Semi-parametric Setup
	6.4 Mathematical Framework: Marked Empirical Processes
		6.4.1 The Basic MEP
		6.4.2 The MEP with Estimated Model Parameters Propagating in a Fixed Direction
		6.4.3 The MEP with Estimated Model Parameters Propagating in an Estimated Direction
	6.5 Mathematical Framework: Bootstrap of Marked Empirical Processes
		6.5.1 Bootstrap of the BMEP
		6.5.2 Bootstrap of the EMEP
	6.6 Exercises
	References
Appendix A boot Package
A.1  Ordinary Bootstrap
A.2  Parametric Bootstrap
A.3  Confidence Intervals
Appendix B simTool Package
Appendix C bootGOF Package
Appendix D Session Info
Index