Approximation theorems of mathematical statistics. (English) Zbl 0538.62002

Serfling, Robert J.

Wiley Series in Probability and Mathematical Statistics. New York etc.: John Wiley & Sons. XIV, 371 p. $ 34.95 (1980).

This book covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of ”probability” theorems to obtain ”statistical” theorems is emphasized. It is hoped that, besides a knowledge of these basic statistical theorems, an appreciation on the instrumental role of probability theory and a perspective on practical needs for its further development may be gained.
A one-semester course each on probability theory and mathematical statistics at the beginning graduate level is presupposed. However, highly polished expertise is not necessary, the treatment here being self-contained at an elementary level. The content is readily accessible to students in statistics, general mathematics, operations research, and selected engineering fields. (From the preface.)
Contents: 1. Preliminary tools and foundations. 2. The basic sample statistics. 3. Transformations of given statistics. 4. Asymptotic theory in parametric inference. 5. U-statistics. 6. Von Mises differentiable statistical functions. 7. M-estimates. 8. L-estimates. 9. R-estimates. 10. Asymptotic relative efficiency. Appendix; References; Index.

MSC:

62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics
62E20	Asymptotic distribution theory in statistics
62G20	Asymptotic properties of nonparametric inference
62F05	Asymptotic properties of parametric tests
62F12	Asymptotic properties of parametric estimators

Keywords:

von Mises functionals; limit theorems; Transformations of given statistics; U-statistics; M-estimates; L-estimates; R-estimates