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Zbl 0538.62002
Serfling, Robert J.
Approximation theorems of mathematical statistics. (English)
[B] 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. \par 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.) \par 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 2000:
*62-01 Textbooks (statistics)
62E20 Asymptotic distribution theory in statistics
62G20 Nonparametric asymptotic efficiency
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

Cited in: Zbl 1001.62005 Zbl 0865.60004 Zbl 0855.62017 Zbl 0771.62001 Zbl 0619.62019

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