Asymptotic Statistics: 3 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 3)

Asymptotic Statistics: 3 (Cambridge Series in Statistical and Probabilistic Mathematics, Series Number 3)

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A. W. van der Vaart
Cambridge University Press
Edition: Illustrated, 9/14/2000
EAN 9780521784504, ISBN10: 0521784506

Paperback, 460 pages, 25.4 x 17.8 x 2.6 cm
Language: English
Originally published in English

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.

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.

'The book is extremely well written and clear ... it is comprehensive and has an abundant supply of worked examples ... anyone who is genuinely interested in learning about some of the recent developments in asymptotic statistics and their potential applications should have a copy of this book.' Biometrics