Asymptotic Statistics

ISBN-13: 9780521784504 / Angielski / Miękka / 2000 / 462 str.

A W van der Vaart

Opis

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.

Recenzje

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

Spis treści

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.