Peter Hall

The Bootstrap and Edgeworth Expansion

• Gebundenes Buch

Produktbeschreibung

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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Produktdetails

• Springer Series in Statistics
• Verlag: Springer, Berlin
• 1992
• Seitenzahl: 372
• Erscheinungstermin: 9. Januar 1992
• Englisch
• Abmessung: 241mm x 160mm x 26mm
• Gewicht: 719g
• ISBN-13: 9780387977201
• ISBN-10: 0387977201
• Artikelnr.: 23594140

Inhaltsangabe

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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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.

Rezensionen

"...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