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

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