An Introduction to Bootstrap Methods with Applications to R.

By: Chernick, Michael RContributor(s): LaBudde, Robert AMaterial type: TextTextPublisher: Somerset : John Wiley & Sons, Incorporated, 2011Copyright date: ©2012Edition: 1st edDescription: 1 online resource (236 pages)Content type: text Media type: computer Carrier type: online resourceISBN: 9781118625453Subject(s): Bootstrap (Statistics) | R (Computer program language)Genre/Form: Electronic books.Additional physical formats: Print version:: An Introduction to Bootstrap Methods with Applications to RDDC classification: 519.544 LOC classification: QA276.8 -- .C478 2011ebOnline resources: Click to View
Contents:
Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- List of Tables -- 1: INTRODUCTION -- 1.1 Historical Background -- 1.2 Definition and Relationship to the Delta Method and Other Resampling Methods -- 1.2.1 Jackknife -- 1.2.2 Delta Method -- 1.2.3 Cross Validation -- 1.2.4 Subsampling -- 1.3 Wide Range of Applications -- 1.4 The Bootstrap and the R Language System -- 1.5 Historical Notes -- 1.6 Exercises -- References -- 2: ESTIMATION -- 2.1 Estimating Bias -- 2.1.1 Bootstrap Adjustment -- 2.1.2 Error Rate Estimation in Discriminant Analysis -- 2.1.3 Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation -- 2.1.4 Patch Data Example -- 2.2 Estimating Location -- 2.2.1 Estimating a Mean -- 2.2.2 Estimating a Median -- 2.3 Estimating Dispersion -- 2.3.1 Estimating an Estimate's Standard Error -- 2.3.2 Estimating Interquartile Range -- 2.4 Linear Regression -- 2.4.1 Overview -- 2.4.2 Bootstrapping Residuals -- 2.4.3 Bootstrapping Pairs (response and Predictor Vector) -- 2.4.4 Heteroscedasticity of Variance: the Wild Bootstrap -- 2.4.5 a Special Class of Linear Regression Models: Multivariable Fractional Polynomials -- 2.5 Nonlinear Regression -- 2.5.1 Examples of Nonlinear Models -- 2.5.2 a Quasi Optical Experiment -- 2.6 Nonparametric Regression -- 2.6.1 Examples of Nonparametric Regression Models -- 2.6.2 Bootstrap Bagging -- 2.7 Historical Notes -- 2.8 Exercises -- References -- 3: CONFIDENCE INTERVALS -- 3.1 Subsampling, Typical Value Theorem, and Efron's Percentile Method -- 3.2 Bootstrap-t -- 3.3 Iterated Bootstrap -- 3.4 Bias Corrected (BC) Bootstrap -- 3.5 Bca and Abc -- 3.6 Tilted Bootstrap -- 3.7 Variance Estimation with Small Sample Sizes -- 3.8 Historical Notes -- 3.9 Exercises -- References -- 4: HYPOTHESIS TESTING -- 4.1 Relationship to Confidence Intervals.
4.2 Why Test Hypotheses Differently? -- 4.3 Tendril Dx Example -- 4.4 Klingenberg Example: Binary Dose-response -- 4.5 Historical Notes -- 4.6 Exercises -- References -- 5: TIME SERIES -- 5.1 Forecasting Methods -- 5.2 Time Domain Models -- 5.3 Can Bootstrapping Improve Prediction Intervals? -- 5.4 Model Based Methods -- 5.4.1 Bootstrapping Stationary Autoregressive Processes -- 5.4.2 Bootstrapping Explosive Autoregressive Processes -- 5.4.3 Bootstrapping Unstable Autoregressive Processes -- 5.4.4 Bootstrapping Stationary Arma Processes -- 5.5 Block Bootstrapping for Stationary Time Series -- 5.6 Dependent Wild Bootstrap (DWB) -- 5.7 Frequency-based Approaches for Stationary Time Series -- 5.8 Sieve Bootstrap -- 5.9 Historical Notes -- 5.10 Exercises -- References -- 6: BOOTSTRAP VARIANTS -- 6.1 Bayesian Bootstrap -- 6.2 Smoothed Bootstrap -- 6.3 Parametric Bootstrap -- 6.4 Double Bootstrap -- 6.5 the M-out-of-n Bootstrap -- 6.6 the Wild Bootstrap -- 6.7 Historical Notes -- 6.8 Exercise -- References -- 7: CHAPTER SPECIAL TOPICS -- 7.1 Spatial Data -- 7.1.1 Kriging -- 7.1.2 Asymptotics for Spatial Data -- 7.1.3 Block Bootstrap on Regular Grids -- 7.1.4 Block Bootstrap on Irregular Grids -- 7.2 Subset Selection in Regression -- 7.2.1 Gong's Logistic Regression Example -- 7.2.2 Gunter's Qualitative Interaction Example -- 7.3 Determining the Number of Distributions in a Mixture -- 7.4 Censored Data -- 7.5 P-value Adjustment -- 7.5.1 the Westfall-young Approach -- 7.5.2 Passive Plus Example -- 7.5.3 Consulting Example -- 7.6 Bioequivalence -- 7.6.1 Individual Bioequivalence -- 7.6.2 Population Bioequivalence -- 7.7 Process Capability Indices -- 7.8 Missing Data -- 7.9 Point Processes -- 7.10 Bootstrap to Detect Outliers -- 7.11 Lattice Variables.
7.12 Covariate Adjustment of Area Under the Curve Estimates for Receiver Operating Characteristic (ROC) Curves -- 7.13 Bootstrapping in Sas -- 7.14 Historical Notes -- 7.15 Exercises -- References -- 8: WHEN THE BOOTSTRAP IS INCONSISTENT AND HOW TO REMEDY IT -- 8.1 Too Small of a Sample Size -- 8.2 Distributions with Infinite Second Moments -- 8.2.1 Introduction -- 8.2.2 Example of Inconsistency -- 8.2.3 Remedies -- 8.3 Estimating Extreme Values -- 8.3.1 Introduction -- 8.3.2 Example of Inconsistency -- 8.3.3 Remedies -- 8.4 Survey Sampling -- 8.4.1 Introduction -- 8.4.2 Example of Inconsistency -- 8.4.3 Remedies -- 8.5 M-dependent Sequences -- 8.5.1 Introduction -- 8.5.2 Example of Inconsistency When Independence Is Assumed -- 8.5.3 Remedy -- 8.6 Unstable Autoregressive Processes -- 8.6.1 Introduction -- 8.6.2 Example of Inconsistency -- 8.6.3 Remedies -- 8.7 Long Range Dependence -- 8.7.1 Introduction -- 8.7.2 Example of Inconsistency -- 8.7.3 a Remedy -- 8.8 Bootstrap Diagnostics -- 8.9 Historical Notes -- 8.10 Exercise -- References -- Author Index -- Subject Index.
Summary: 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 insightfulSummary: reference for practitioners working with data in engineering, medicine, and the social sciences who would like to acquire a basic understanding of bootstrap methods.
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Cover -- Title Page -- Copyright -- Contents -- Preface -- Acknowledgments -- List of Tables -- 1: INTRODUCTION -- 1.1 Historical Background -- 1.2 Definition and Relationship to the Delta Method and Other Resampling Methods -- 1.2.1 Jackknife -- 1.2.2 Delta Method -- 1.2.3 Cross Validation -- 1.2.4 Subsampling -- 1.3 Wide Range of Applications -- 1.4 The Bootstrap and the R Language System -- 1.5 Historical Notes -- 1.6 Exercises -- References -- 2: ESTIMATION -- 2.1 Estimating Bias -- 2.1.1 Bootstrap Adjustment -- 2.1.2 Error Rate Estimation in Discriminant Analysis -- 2.1.3 Simple Example of Linear Discrimination and Bootstrap Error Rate Estimation -- 2.1.4 Patch Data Example -- 2.2 Estimating Location -- 2.2.1 Estimating a Mean -- 2.2.2 Estimating a Median -- 2.3 Estimating Dispersion -- 2.3.1 Estimating an Estimate's Standard Error -- 2.3.2 Estimating Interquartile Range -- 2.4 Linear Regression -- 2.4.1 Overview -- 2.4.2 Bootstrapping Residuals -- 2.4.3 Bootstrapping Pairs (response and Predictor Vector) -- 2.4.4 Heteroscedasticity of Variance: the Wild Bootstrap -- 2.4.5 a Special Class of Linear Regression Models: Multivariable Fractional Polynomials -- 2.5 Nonlinear Regression -- 2.5.1 Examples of Nonlinear Models -- 2.5.2 a Quasi Optical Experiment -- 2.6 Nonparametric Regression -- 2.6.1 Examples of Nonparametric Regression Models -- 2.6.2 Bootstrap Bagging -- 2.7 Historical Notes -- 2.8 Exercises -- References -- 3: CONFIDENCE INTERVALS -- 3.1 Subsampling, Typical Value Theorem, and Efron's Percentile Method -- 3.2 Bootstrap-t -- 3.3 Iterated Bootstrap -- 3.4 Bias Corrected (BC) Bootstrap -- 3.5 Bca and Abc -- 3.6 Tilted Bootstrap -- 3.7 Variance Estimation with Small Sample Sizes -- 3.8 Historical Notes -- 3.9 Exercises -- References -- 4: HYPOTHESIS TESTING -- 4.1 Relationship to Confidence Intervals.

4.2 Why Test Hypotheses Differently? -- 4.3 Tendril Dx Example -- 4.4 Klingenberg Example: Binary Dose-response -- 4.5 Historical Notes -- 4.6 Exercises -- References -- 5: TIME SERIES -- 5.1 Forecasting Methods -- 5.2 Time Domain Models -- 5.3 Can Bootstrapping Improve Prediction Intervals? -- 5.4 Model Based Methods -- 5.4.1 Bootstrapping Stationary Autoregressive Processes -- 5.4.2 Bootstrapping Explosive Autoregressive Processes -- 5.4.3 Bootstrapping Unstable Autoregressive Processes -- 5.4.4 Bootstrapping Stationary Arma Processes -- 5.5 Block Bootstrapping for Stationary Time Series -- 5.6 Dependent Wild Bootstrap (DWB) -- 5.7 Frequency-based Approaches for Stationary Time Series -- 5.8 Sieve Bootstrap -- 5.9 Historical Notes -- 5.10 Exercises -- References -- 6: BOOTSTRAP VARIANTS -- 6.1 Bayesian Bootstrap -- 6.2 Smoothed Bootstrap -- 6.3 Parametric Bootstrap -- 6.4 Double Bootstrap -- 6.5 the M-out-of-n Bootstrap -- 6.6 the Wild Bootstrap -- 6.7 Historical Notes -- 6.8 Exercise -- References -- 7: CHAPTER SPECIAL TOPICS -- 7.1 Spatial Data -- 7.1.1 Kriging -- 7.1.2 Asymptotics for Spatial Data -- 7.1.3 Block Bootstrap on Regular Grids -- 7.1.4 Block Bootstrap on Irregular Grids -- 7.2 Subset Selection in Regression -- 7.2.1 Gong's Logistic Regression Example -- 7.2.2 Gunter's Qualitative Interaction Example -- 7.3 Determining the Number of Distributions in a Mixture -- 7.4 Censored Data -- 7.5 P-value Adjustment -- 7.5.1 the Westfall-young Approach -- 7.5.2 Passive Plus Example -- 7.5.3 Consulting Example -- 7.6 Bioequivalence -- 7.6.1 Individual Bioequivalence -- 7.6.2 Population Bioequivalence -- 7.7 Process Capability Indices -- 7.8 Missing Data -- 7.9 Point Processes -- 7.10 Bootstrap to Detect Outliers -- 7.11 Lattice Variables.

7.12 Covariate Adjustment of Area Under the Curve Estimates for Receiver Operating Characteristic (ROC) Curves -- 7.13 Bootstrapping in Sas -- 7.14 Historical Notes -- 7.15 Exercises -- References -- 8: WHEN THE BOOTSTRAP IS INCONSISTENT AND HOW TO REMEDY IT -- 8.1 Too Small of a Sample Size -- 8.2 Distributions with Infinite Second Moments -- 8.2.1 Introduction -- 8.2.2 Example of Inconsistency -- 8.2.3 Remedies -- 8.3 Estimating Extreme Values -- 8.3.1 Introduction -- 8.3.2 Example of Inconsistency -- 8.3.3 Remedies -- 8.4 Survey Sampling -- 8.4.1 Introduction -- 8.4.2 Example of Inconsistency -- 8.4.3 Remedies -- 8.5 M-dependent Sequences -- 8.5.1 Introduction -- 8.5.2 Example of Inconsistency When Independence Is Assumed -- 8.5.3 Remedy -- 8.6 Unstable Autoregressive Processes -- 8.6.1 Introduction -- 8.6.2 Example of Inconsistency -- 8.6.3 Remedies -- 8.7 Long Range Dependence -- 8.7.1 Introduction -- 8.7.2 Example of Inconsistency -- 8.7.3 a Remedy -- 8.8 Bootstrap Diagnostics -- 8.9 Historical Notes -- 8.10 Exercise -- References -- Author Index -- Subject Index.

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.

Description based on publisher supplied metadata and other sources.

Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2018. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.

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