Asymptotic Statistics

"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

'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

A mathematically rigorous, practical introduction presenting standard topics plus research.

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.

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 text for a graduate or Master's level statistics course, this book will also serve as a reference for researchers in statistics, probability, and their applications.

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.