Theory of statistical inference and information. Transl. from the Slovak by the author. (English) Zbl 0711.62002

Vajda, Igor

Theory and Decision Library, Series B: Mathematical and Statistical Methods, 11. Dordrecht etc.: Kluwer Academic Publishers. 432 p. Dfl. 305.00; $ 149.00; £95.00 (1989).

The book presents a basic theory of statistical inference and information with emphasis on methods of convex analysis common for mathematical statistics and information theory. The level of mathematics used is based on abstract measurable spaces wherefore the book is best suited for postgraduate and advanced undergraduate courses on the topic.
The book studies systematically convex functions of measures in general, and convex functions of probability measures in particular. Distances of probability measures used in mathematical statistics and information theory are examples of these convex functions. Applications of these functions in mathematical statistics and information theory (e.g. concepts of information, Bayes risk, entropy, Kantorovich-Vasershtein and Ornstein distances, etc.) are in a central role in the book. Common tools used in and relations existing between mathematical statistics and information theory are considered systematically.

Reviewer: J.Virtanen

MSC:

62B10	Statistical aspects of information-theoretic topics
62-01	Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics

Keywords:

Kantorovich-Vasershtein distance; statistical inference; convex functions of measures; Distances of probability measures; information; Bayes risk; entropy; Ornstein distances