Asymptotic Statistics / Edition 1

by A. W. van der Vaart

Overview

Here is a practical and mathematically rigorous introduction to the field of asymptotic statistics. In addition to most of the standard topics of an asymptotics course—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, one of the book's unifying themes that mainly entails the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation.

Product Details

ISBN-13:	9780521784504
Publisher:	Cambridge University Press
Publication date:	06/19/2000
Series:	Cambridge Series in Statistical and Probabilistic Mathematics , #3
Edition description:	New Edition
Pages:	462
Product dimensions:	7.05(w) x 10.04(h) x 1.10(d)

Table of Contents

1. Introduction; 2. Stochastic convergence; 3. The Δ-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 Δ-method; 21. Quantiles and order statistics; 22. L-statistics; 23. The bootstrap; 24. Nonparametric density estimation; 25. Semiparametric models.

Editorial Reviews

'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

'I recommend this book to every advanced Master's student, Ph.D. student or researcher in mathematical statistics.' Kwantitatieve methoden

From the Publisher