Statistical decision theory and Bayesian analysis. 2nd ed. (English) Zbl 0572.62008

Berger, James O.

Springer Series in Statistics. New York etc.: Springer-Verlag. XVI, 617 p. DM 128.00 (1985).

[For a review of the first, 1980 edition see Zbl 0444.62009.]
This second edition of the book has undergone a title change, with the addition of ”Bayesian analysis”. This reflects the major change in the book, namely an extensive upgrading of the Bayesian material, to the point where the book can serve as a text on Bayesian analysis alone.
For those familiar with the old book, the greatest changes are in chapters 3 and 4, which were substantially enlarged and almost completely rewritten. Some sections of chapter 1 were redone (particularly 1.6), and some small subsections were added to chapter 2. The only significant change to chapter 5 was the inclusion of an introduction to the now vast field of minimax multivariate estimation (Stein estimation); this has become by far the largest statistical area of development within minimax theory.
Only very minor changes were made to chapter 6, and chapter 7 was changed only by the addition of a section discussing the issue of optimal stopping. A number of changes were made to chapter 8, in light of recent developments, but no thorough survey was attempted.

MSC:

62C10	Bayesian problems; characterization of Bayes procedures
62Cxx	Statistical decision theory
62L10	Sequential statistical analysis
62-02	Research exposition (monographs, survey articles) pertaining to statistics
62A01	Foundations and philosophical topics in statistics
62F15	Bayesian inference

Keywords:

subjective probability; empirical Bayes; robustness; minimax multivariate estimation; Stein estimation; optimal stopping

Citations:

Zbl 0444.62009