Asymptotic statistics

by Vaart, A. W. van der

Type Book

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Title Statements

Full title :Asymptotic statistics / A.W. van der Vaart.

Summary

This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics.

Edition Statements

Publication Date:1998.

Publication Statements

Publisher(s):Cambridge University Press
Place of Publication:Cambridge, UK
Language:eng
Publication Date:1998.

The Physical Object

Description:1 online resource (xv, 443 pages) : : illustrations

Edition Identifiers

ISBN:9780511802256, 0511802250, 9781107263727, 1107263727
oclc:ocn817928380
LC Classification:QA276
Dewey Decimal:519.5

1. Introduction -- 2. Stochastic convergence -- 3. The delta-method -- 4. Moment estimators -- 5. M- and Z-estimators -- 6. Contiguity -- 7. Local asymptotic normality -- 8. Efficiency of estimators -- 9. Limits of experiments -- 10. Bayes procedures -- 11. Projections -- 12. U-statistics -- 13. Rank, sign, and permutation statistics -- 14. Relative efficiency of tests -- 15. Efficiency of tests -- 16. Likelihood ratio tests -- 17. Chi-square tests -- 18. Stochastic convergence in metric spaces -- 19. Empirical processes -- 20. The functional delta-method -- 21. Quantiles and order statistics -- 22. L-statistics -- 23. The bootstrap -- 24. Nonparametric density estimation -- 25. Semiparametric models.

Subjects

Asymptotische analyse Asymptotische Statistik Mathematical statistics -- Asymptotic t… Statistics Statistics as Topic statistiek Statistique mathématique -- Théorie asy… Statistiques