Synopses & Reviews
The aim of this book is to present a readable introduction to the theory of bootstrap methods which is suitable for graduate students and research workers in statistics. In particular, the author discusses the application of bootstrap methods to linear regression, non-parametric regression and density estimation. The author's perspective is that the Edgeworth expansion sheds important light on the performance of bootstrap methods and that, conversely, bootstrap methods motivate a renewed interest in the study of the Edgeworth expansion. Consequently, the book is structured to first present chapters which introduce the basic concepts of bootstrap methods and the Edgeworth expansion. Subsequent chapters then explore the interaction between the two subjects and their application to statistical techniques. Generally, technical details are deferred to the last chapter so as to enable a reader with a relatively small exposure to theoretical statistics to enjoy this account of a rapidly growing branch of statistical research.
Review
"...an up-to-date and comprehensive account of the title theme...provides a path to several major research frontiers in the bootstrap literature." - Journal of the American Statistical Association
Synopsis
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.
Synopsis
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.
Table of Contents
Principles of bootstrap methodology.- Principles of Edgeworth expansion.- An Edgeworth view of the bootstrap; Bootstrap curve estimation.- Details of mathematical rigour; Appendices.