Synopses & Reviews
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.
Review
"There have been a number of attempts to present the theory of contiguity and limits of experiments as the basis for the most general results in the asymptotic theory of statistics, but this is by good measure the most successful...very elegantly written...the writing style is clear and concise, and the explanatory material is excellent...courses that could be taught using this book as a guide: a first course in asymptotic theory, a course on the use of empirical processes in statistics, or part of a course on nonparametric theory. A research seminar could also be built around Chapter 25...This book would also be an excellent reference for researchers familiar with some of the material, but wanting an overview of modern rigorous treatments of asymptotic theory." Mathematical Reviews
Synopsis
A mathematically rigorous, practical introduction presenting standard topics plus more recent research.
Synopsis
This mathematically rigorous, practical introduction to the field of asymptotic statistics develops most of the usual topics of an asymptotics course, and also presents recent research topics such as empirical processes, the bootstrap, and semiparametric models.
Synopsis
This book is an introduction to the field of asymptotic statistics. The treatment is mathematically rigorous but practical rather than simply technical. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. In addition to the usual topics of an asymptotics course, the author also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes. Suitable as a graduate or Master's level statistics test, this book will also serve as a reference for researchers.
Table of Contents
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.