This monograph addresses two quite different topics, each being able to shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap. The book is aimed at graduate level for those with some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter such that mathematically able readers without knowledge of the rigorous theory of probability will have no trouble understanding most of the book.

This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems.

Statistics is a subject of many uses and surprisingly few effective practitioners. The traditional road to statistical knowledge is blocked, for most, by a formidable wall of mathematics. The approach in An Introduction to the Bootstrap avoids that wall. It arms scientists and engineers, as well as statisticians, with the computational techniques they need to analyze and understand complicated data sets.

This monograph addresses two quite different topics, each being able to shed light on the other. Firstly, it lays the foundation for a particular view of the bootstrap. Secondly, it gives an account of Edgeworth expansion. The first two chapters deal with the bootstrap and Edgeworth expansion respectively, while chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properties of the bootstrap. The book is aimed at graduate level for those with some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter such that mathematically able readers without knowledge of the rigorous theory of probability will have no trouble understanding most of the book.

By giving a detailed account of bootstrap methods and their properties for dependent data, this book provides illustrative numerical examples throughout. The book fills a gap in the literature covering research on re-sampling methods for dependent data that has witnessed vigorous growth over the last two decades but remains scattered in various statistics and econometrics journals. It can be used as a graduate level text and also as a research monograph for statisticians and econometricians.

Since Efron's profound paper on the bootstrap, an enormous amount of effort has been spent on the development of bootstrap, jacknife, and other resampling methods. The primary goal of these computer-intensive methods has been to provide statistical tools that work in complex situations without imposing unrealistic or unverifiable assumptions about the data generating mechanism. This book sets out to lay some of the foundations for subsampling methodology and related methods.

INTRODUCTION 1) Introduction In 1979, Efron introduced the bootstrap method as a kind of universal tool to obtain approximation of the distribution of statistics. The now well known underlying idea is the following : consider a sample X of Xl ' n independent and identically distributed H.i.d.) random variables (r. v,'s) with unknown probability measure (p.m.) P . Assume we are interested in approximating the distribution of a statistical functional T(P ) the -1 nn empirical counterpart of the functional T(P) , where P n := n l:i=l aX. is 1 the empirical p.m. Since in some sense P is close to P when n is large, n • • LLd. from P and builds the empirical p.m. if one samples Xl ' ... , Xm n n -1 mn • • P T(P ) conditionally on := mn l: i =1 a • ' then the behaviour of P m n,m n n n X. 1 T(P ) should imitate that of when n and mn get large. n This idea has lead to considerable investigations to see when it is correct, and when it is not. When it is not, one looks if there is any way to adapt it.

A practical and accessible introduction to the bootstrap method——newly revised and updated Over the past decade, the application of bootstrap methods to new areas of study has expanded, resulting in theoretical and applied advances across various fields. Bootstrap Methods, Second Edition is a highly approachable guide to the multidisciplinary, real-world uses of bootstrapping and is ideal for readers who have a professional interest in its methods, but are without an advanced background in mathematics. Updated to reflect current techniques and the most up-to-date work on the topic, the Second Edition features: The addition of a second, extended bibliography devoted solely to publications from 1999–2007, which is a valuable collection of references on the latest research in the field A discussion of the new areas of applicability for bootstrap methods, including use in the pharmaceutical industry for estimating individual and population bioequivalence in clinical trials A revised chapter on when and why bootstrap fails and remedies for overcoming these drawbacks Added coverage on regression, censored data applications, P-value adjustment, ratio estimators, and missing data New examples and illustrations as well as extensive historical notes at the end of each chapter With a strong focus on application, detailed explanations of methodology, and complete coverage of modern developments in the field, Bootstrap Methods, Second Edition is an indispensable reference for applied statisticians, engineers, scientists, clinicians, and other practitioners who regularly use statistical methods in research. It is also suitable as a supplementary text for courses in statistics and resampling methods at the upper-undergraduate and graduate levels.

Disk contains the library functions and documentation for use with Splus for Windows.

A hands-on guide to using R to carry out key statistical practices in educational and behavioral sciences research Computing has become an essential part of the day-to-day practice of statistical work, broadening the types of questions that can now be addressed by research scientists applying newly derived data analytic techniques. Comparing Groups: Randomization and Bootstrap Methods Using R emphasizes the direct link between scientific research questions and data analysis. Rather than relying on mathematical calculations, this book focus on conceptual explanations and the use of statistical computing in an effort to guide readers through the integration of design, statistical methodology, and computation to answer specific research questions regarding group differences. Utilizing the widely-used, freely accessible R software, the authors introduce a modern approach to promote methods that provide a more complete understanding of statistical concepts. Following an introduction to R, each chapter is driven by a research question, and empirical data analysis is used to provide answers to that question. These examples are data-driven inquiries that promote interaction between statistical methods and ideas and computer application. Computer code and output are interwoven in the book to illustrate exactly how each analysis is carried out and how output is interpreted. Additional topical coverage includes: Data exploration of one variable and multivariate data Comparing two groups and many groups Permutation tests, randomization tests, and the independent samples t-Test Bootstrap tests and bootstrap intervals Interval estimates and effect sizes Throughout the book, the authors incorporate data from real-world research studies as well aschapter problems that provide a platform to perform data analyses. A related Web site features a complete collection of the book's datasets along with the accompanying codebooks and the R script files and commands, allowing readers to reproduce the presented output and plots. Comparing Groups: Randomization and Bootstrap Methods Using R is an excellent book for upper-undergraduate and graduate level courses on statistical methods, particularlyin the educational and behavioral sciences. The book also serves as a valuable resource for researchers who need a practical guide to modern data analytic and computational methods.