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An Introduction to Bootstrap Methods with Applications to R

Book Description

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. 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.

Table of Contents

  1. Cover Page
  2. Title Page
  3. Copyright
  4. Contents
  5. PREFACE
  6. ACKNOWLEDGMENTS
  7. LIST OF TABLES
  8. 1: INTRODUCTION
    1. 1.1 HISTORICAL BACKGROUND
    2. 1.2 DEFINITION AND RELATIONSHIP TO THE DELTA METHOD AND OTHER RESAMPLING METHODS
    3. 1.3 WIDE RANGE OF APPLICATIONS
    4. 1.4 THE BOOTSTRAP AND THE R LANGUAGE SYSTEM
    5. 1.5 HISTORICAL NOTES
    6. 1.6 EXERCISES
    7. REFERENCES
  9. 2: ESTIMATION
    1. 2.1 ESTIMATING BIAS
    2. 2.2 ESTIMATING LOCATION
    3. 2.3 ESTIMATING DISPERSION
    4. 2.4 LINEAR REGRESSION
    5. 2.5 NONLINEAR REGRESSION
    6. 2.6 NONPARAMETRIC REGRESSION
    7. 2.7 Historical Notes
    8. 2.8 EXERCISES
    9. REFERENCES
  10. 3: CONFIDENCE INTERVALS
    1. 3.1 SUBSAMPLING, TYPICAL VALUE THEOREM, AND EFRON'S PERCENTILE METHOD
    2. 3.2 BOOTSTRAP-T
    3. 3.3 ITERATED BOOTSTRAP
    4. 3.4 BIAS-CORRECTED (BC) BOOTSTRAP
    5. 3.5 BCa AND ABC
    6. 3.6 TILTED BOOTSTRAP
    7. 3.7 VARIANCE ESTIMATION WITH SMALL SAMPLE SIZES
    8. 3.8 HISTORICAL NOTES
    9. 3.9 EXERCISES
    10. REFERENCES
  11. 4: HYPOTHESIS TESTING
    1. 4.1 RELATIONSHIP TO CONFIDENCE INTERVALS
    2. 4.2 WHY TEST HYPOTHESES DIFFERENTLY?
    3. 4.3 TENDRIL DX EXAMPLE
    4. 4.4 KLINGENBERG EXAMPLE: BINARY DOSE-RESPONSE
    5. 4.5 HISTORICAL NOTES
    6. 4.6 EXERCISES
    7. REFERENCES
  12. 5: TIME SERIES
    1. 5.1 FORECASTING METHODS
    2. 5.2 TIME DOMAIN MODELS
    3. 5.3 CAN BOOTSTRAPPING IMPROVE PREDICTION INTERVALS?
    4. 5.4 MODEL-BASED METHODS
    5. 5.4.2 Bootstrapping Explosive Autoregressive Processes
    6. 5.5 BLOCK BOOTSTRAPPING FOR STATIONARY TIME SERIES
    7. 5.6 DEPENDENT WILD BOOTSTRAP (DWB)
    8. 5.7 FREQUENCY-BASED APPROACHES FOR STATIONARY TIME SERIES
    9. 5.8 SIEVE BOOTSTRAP
    10. 5.9 HISTORICAL NOTES
    11. 5.10 EXERCISES
    12. REFERENCES
  13. 6: BOOTSTRAP VARIANTS
    1. 6.1 BAYESIAN BOOTSTRAP
    2. 6.2 SMOOTHED BOOTSTRAP
    3. 6.3 PARAMETRIC BOOTSTRAP
    4. 6.4 DOUBLE BOOTSTRAP
    5. 6.5 THE M -OUT-OF- N BOOTSTRAP
    6. 6.6 THE WILD BOOTSTRAP
    7. 6.7 HISTORICAL NOTES
    8. 6.8 EXERCISE
    9. REFERENCES
  14. 7: CHAPTER SPECIAL TOPICS
    1. 7.1 SPATIAL DATA
    2. 7.2 SUBSET SELECTION IN REGRESSION
    3. 7.3 DETERMINING THE NUMBER OF DISTRIBUTIONS IN A MIXTURE
    4. 7.4 CENSORED DATA
    5. 7.5 P -VALUE ADJUSTMENT
    6. 7.6 BIOEQUIVALENCE
    7. 7.7 PROCESS CAPABILITY INDICES
    8. 7.8 MISSING DATA
    9. 7.9 POINT PROCESSES
    10. 7.10 BOOTSTRAP TO DETECT OUTLIERS
    11. 7.11 LATTICE VARIABLES
    12. 7.12 COVARIATE ADJUSTMENT OF AREA UNDER THE CURVE ESTIMATES FOR RECEIVER OPERATING CHARACTERISTIC (ROC) CURVES
    13. 7.13 BOOTSTRAPPING IN SAS
    14. 7.14 HISTORICAL NOTES
    15. 7.15 EXERCISES
    16. REFERENCES
  15. 8: WHEN THE BOOTSTRAP IS INCONSISTENT AND HOW TO REMEDY IT
    1. 8.1 TOO SMALL OF A SAMPLE SIZE
    2. 8.2 DISTRIBUTIONS WITH INFINITE SECOND MOMENTS
    3. 8.3 ESTIMATING EXTREME VALUES
    4. 8.4 SURVEY SAMPLING
    5. 8.4.1 Introduction
    6. 8.5 M-DEPENDENT SEQUENCES
    7. 8.6 UNSTABLE AUTOREGRESSIVE PROCESSES
    8. 8.7 LONG-RANGE DEPENDENCE
    9. 8.8 BOOTSTRAP DIAGNOSTICS
    10. 8.9 HISTORICAL NOTES
    11. 8.10 EXERCISE
    12. REFERENCES
  16. AUTHOR INDEX
  17. SUBJECT INDEX