The Bootstrap and Edgeworth Expansion (häftad)
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Format
Häftad (Paperback / softback)
Språk
Engelska
Antal sidor
354
Utgivningsdatum
1995-05-01
Upplaga
1st ed. 1995. Corr. 2nd printing 1997
Förlag
Springer-Verlag New York Inc.
Medarbetare
Bickel, P. (red.)
Illustrationer
XIV, 354 p.
Dimensioner
235 x 155 x 20 mm
Vikt
520 g
Antal komponenter
1
Komponenter
1 Paperback / softback
ISBN
9780387945088

The Bootstrap and Edgeworth Expansion

av Peter Hall
Häftad,  Engelska, 1995-05-01
1873
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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.
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"...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

Innehållsförteckning

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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