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AuthorHall, Peter. author
TitleThe Bootstrap and Edgeworth Expansion [electronic resource] / by Peter Hall
ImprintNew York, NY : Springer New York : Imprint: Springer, 1992
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Descript XIV, 354 p. online resource


This monograph addresses two quite different topics, in the belief that each can 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. Chapter 1 is about the bootstrap, witih almost no mention of Edgeworth expansion; Chapter 2 is about Edgeworth expansion, with scarcely a word about the bootstrap; and Chapters 3 and 4 bring these two themes together, using Edgeworth expansion to explore and develop the properites of the bootstrap. The book is aimed a a graduate level audience who has some exposure to the methods of theoretical statistics. However, technical details are delayed until the last chapter (entitled "Details of Mathematical Rogour"), and so a mathematically able reader without knowledge of the rigorous theory of probability will have no trouble understanding the first four-fifths of the book. The book simultaneously fills two gaps in the literature; it provides a very readable graduate level account of the theory of Edgeworth expansion, and it gives a detailed introduction to the theory of bootstrap methods


1: Principles of Bootstrap Methodology -- 2: Principles of Edgeworth Expansion -- 3: An Edgeworth View of the Bootstrap -- 4: Bootstrap Curve Estimation -- 5: Details of Mathematical Rigour -- Appendix I: Number and Sizes of Atoms of Nonparametric Bootstrap Distribution -- Appendix II: Monte Carlo Simulation -- II.1 Introduction -- II.2 Uniform Resampling -- II.3 Linear Approximation -- II.4 Centring Method -- II.5 Balanced Resampling -- II.6 Antithetic Resampling -- II.7 Importance Resampling -- II.7.1 Introduction -- II.7.2 Concept of Importance Resampling -- II.7.3 Importance Resampling for Approximating Bias, Variance, Skewness, etc. -- II.7.4 Importance Resampling for a Distribution Function -- II.8 Quantile Estimation -- Appendix III: Confidence Pictures -- Appendix IV: A Non-Standard Example: Quantite Error Estimation -- IV. 1 Introduction -- IV.2 Definition of the Mean Squared Error Estimate -- IV.3 Convergence Rate of the Mean Squared Error Estimate -- IV.4 Edgeworth Expansions for the Studentized Bootstrap Quantile Estimate -- Appendix V: A Non-Edgeworth View of the Bootstrap -- References -- Author Index

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