Introduction to Bootstrap Methods With Applications to R

Informationen zum Autor MICHAEL R. CHERNICK, PhD, is Manager of Biostatistical Services at Lankenau Institute for Medical Research, where he conducts statistical design and analysis for pharmaceutical research. He has more than thirty years of experience in the application of statistical methods to such areas as medicine, energy, engineering, insurance, and pharmaceuticals. Dr. Chernick is the author of Bootstrap Methods: A Guide for Practitioners and Researchers, Second Edition and The Essentials of Biostatistics for Physicians, Nurses, and Clinicians, and the coauthor of Introductory Biostatistics for the Health Sciences: Modern Applications Including Bootstrap, all published by Wiley.ROBERT A. LaBUDDE, PhD, is President of Least Cost Formulations, Ltd., a mathematical software development company that specializes in optimization and process control software for manufacturing companies. He has extensive experience in industry and academia and currently serves as Adjunct Associate Professor in the Department of Mathematics and Statistics at Old Dominion University. Klappentext A comprehensive introduction to bootstrap methods in the R programming environmentBootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. An Introduction to Bootstrap Methods with Applications to R explores the practicality of this approach and successfully utilizes R to illustrate applications for the bootstrap and other resampling methods. This book provides a modern introduction to bootstrap methods for readers who do not have an extensive background in advanced mathematics. Emphasis throughout is on the use of bootstrap methods as an exploratory tool, including its value in variable selection and other modeling environments.The authors begin with a description of bootstrap methods and its relationship to other resampling methods, along with an overview of the wide variety of applications of the approach. Subsequent chapters offer coverage of improved confidence set estimation, estimation of error rates in discriminant analysis, and applications to a wide variety of hypothesis testing and estimation problems, including pharmaceutical, genomics, and economics. To inform readers on the limitations of the method, the book also exhibits counterexamples to the consistency of bootstrap methods.An introduction to R programming provides the needed preparation to work with the numerous exercises and applications presented throughout the book. A related website houses the book's R subroutines, and an extensive listing of references provides resources for further study.Discussing the topic at a remarkably practical and accessible level, An Introduction to Bootstrap Methods with Applications to R is an excellent book for introductory courses on bootstrap and resampling methods at the upper-undergraduate and graduate levels. It also serves as an insightful reference for practitioners working with data in engineering, medicine, and the social sciences who would like to acquire a basic understanding of bootstrap methods. Zusammenfassung A comprehensive introduction to bootstrap methods in the R programming environment Bootstrap methods provide a powerful approach to statistical data analysis, as they have more general applications than standard parametric methods. Inhaltsverzeichnis PREFACE xiACKNOWLEDGMENTS xvLIST OF TABLES xvii1 INTRODUCTION 11.1 Historical Background 11.2 Definition and Relationship to the Delta Method and Other Resampling Methods 31.2.1 Jackknife 61.2.2 Delta Method 71.2.3 Cross-Validation 71.2.4 Subsampling 81.3 Wide Range of Applications 81.4 The Bootstrap and the R Language System 101.5 Historical Notes 251.6 Exercises 26References 272 ESTIMATION 302.1 Estimating Bias 302.1.1 Bootstrap Adjustment 302.1.2 Error Rate Estimation in Discriminant Analysis 322.1....

List of contents

PREFACE xi
 
ACKNOWLEDGMENTS xv
 
LIST OF TABLES xvii
 
1 INTRODUCTION 1
 
1.1 Historical Background 1
 
1.2 Definition and Relationship to the Delta Method and Other Resampling Methods 3
 
1.2.1 Jackknife 6
 
1.2.2 Delta Method 7
 
1.2.3 Cross-Validation 7
 
1.2.4 Subsampling 8
 
1.3 Wide Range of Applications 8
 
1.4 The Bootstrap and the R Language System 10
 
1.5 Historical Notes 25
 
1.6 Exercises 26
 
References 27
 
2 ESTIMATION 30
 
2.1 Estimating Bias 30
 
2.1.1 Bootstrap Adjustment 30
 
2.1.2 Error Rate Estimation in Discriminant Analysis 32
 
2.1.3 Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation 42
 
2.1.4 Patch Data Example 51
 
2.2 Estimating Location 53
 
2.2.1 Estimating a Mean 53
 
2.2.2 Estimating a Median 54
 
2.3 Estimating Dispersion 54
 
2.3.1 Estimating an Estimate's Standard Error 55
 
2.3.2 Estimating Interquartile Range 56
 
2.4 Linear Regression 56
 
2.4.1 Overview 56
 
2.4.2 Bootstrapping Residuals 57
 
2.4.3 Bootstrapping Pairs (Response and Predictor Vector) 58
 
2.4.4 Heteroscedasticity of Variance: The Wild Bootstrap 58
 
2.4.5 A Special Class of Linear Regression Models: Multivariable Fractional Polynomials 60
 
2.5 Nonlinear Regression 60
 
2.5.1 Examples of Nonlinear Models 61
 
2.5.2 A Quasi-Optical Experiment 63
 
2.6 Nonparametric Regression 63
 
2.6.1 Examples of Nonparametric Regression Models 64
 
2.6.2 Bootstrap Bagging 66
 
2.7 Historical Notes 67
 
2.8 Exercises 69
 
References 71
 
3 CONFIDENCE INTERVALS 76
 
3.1 Subsampling, Typical Value Theorem, and Efron's Percentile Method 77
 
3.2 Bootstrap-t 79
 
3.3 Iterated Bootstrap 83
 
3.4 Bias-Corrected (BC) Bootstrap 85
 
3.5 BCa and ABC 85
 
3.6 Tilted Bootstrap 88
 
3.7 Variance Estimation with Small Sample Sizes 90
 
3.8 Historical Notes 94
 
3.9 Exercises 96
 
References 98
 
4 HYPOTHESIS TESTING 101
 
4.1 Relationship to Confi dence Intervals 103
 
4.2 Why Test Hypotheses Differently? 105
 
4.3 Tendril DX Example 106
 
4.4 Klingenberg Example: Binary Dose-Response 108
 
4.5 Historical Notes 109
 
4.6 Exercises 110
 
References 111
 
5 TIME SERIES 113
 
5.1 Forecasting Methods 113
 
5.2 Time Domain Models 114
 
5.3 Can Bootstrapping Improve Prediction Intervals? 115
 
5.4 Model-Based Methods 118
 
5.4.1 Bootstrapping Stationary Autoregressive Processes 118
 
5.4.2 Bootstrapping Explosive Autoregressive Processes 123
 
5.4.3 Bootstrapping Unstable Autoregressive Processes 123
 
5.4.4 Bootstrapping Stationary ARMA Processes 123
 
5.5 Block Bootstrapping for Stationary Time Series 123
 
5.6 Dependent Wild Bootstrap (DWB) 126
 
5.7 Frequency-Based Approaches for Stationary Time Series 127
 
5.8 Sieve Bootstrap 128
 
5.9 Historical Notes 129
 
5.10 Exercises 131
 
References 131
 
6 BOOTSTRAP VARIANTS 136
 
6.1 Bayesian Bootstrap 137
 
6.2 Smoothed Bootstrap 138
 
6.3 Parametric Bootstrap 139
 
6.4 Double Bootstrap 139
 
6.5 The m-Out-of-n Bootstrap 140
 
6.6 The Wild Bootstrap 141
 
6.7 Historical Notes 141
 
6.8 Exercises 142
 
References 142
 
7 CHAPTER SPECIAL TOPICS

Report

"I recommend this text to anyone wishing to apply computationally intensive methods and if you only purchase one book on bootstrap methods then this could be the book for you!." ( International Statistical Review , 2012)

Product details

• Authors: Michael R Chernick, Michael R. Chernick, Michael R. (Lankenau Institute for Medic Chernick, Michael R. (Lankenau Institute for Medical Research) Chernick, Chernick Michael R., Robert A LaBudde, Robert A. LaBudde, Robert A. (Least Cost Formulations Ltd.) LaBudde, LaBudde Robert A.
• Publisher: Wiley, John and Sons Ltd
• Languages: English
• Product format: Hardback
• Released: 02.12.2011
• EAN: 9780470467046
• ISBN: 978-0-470-46704-6
• No. of pages: 240
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Probability theory, stochastic theory, mathematical statistics; Statistik, Stochastik, Statistics, Electrical & Electronics Engineering, Elektrotechnik u. Elektronik, Numerische Methoden u. Algorithmen, Numerical Methods & Algorithms, Angewandte Wahrscheinlichkeitsrechnung u. Statistik, Applied Probability & Statistics, Statistics for Finance, Business & Economics, Finanz- u. Wirtschaftsstatistik