Asymptotic Statistics / Edition 1

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.

ISBN-13: 9780521784504

Media Type: Paperback

Publisher: Cambridge University Press

Publication Date: 06-19-2000

Pages: 462

Product Dimensions: 6.81(w) x 9.09(h) x 1.06(d)

Series: Cambridge Series in Statistical and Probabilistic Mathematic #3

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.