The Bootstrap and Edgeworth Expansion (Springer Series in Statistics) - Brossura

Hall, Peter

Brossura

ISBN 10: 0387945083 ISBN 13: 9780387945088

Casa editrice: Springer, 2005

Riassunto

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.

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Recensione

"...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

Contenuti

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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2005
• Lingua: Inglese
• ISBN 10: 0387945083
• ISBN 13: 9780387945088
• Rilegatura: Copertina flessibile
• Numero di pagine: 372
• Contatto del produttore: non disponibile
• Persona responsabile: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3,69115 Heidelberg, Germany; Heidelberg; 69115; Germania