Pitman’s measure of closeness: a comparison of statistical estimators. (English) Zbl 0779.62019

Philadelphia, PA: SIAM, Society for Industrial and Applied Mathematics. xv, 226 p. (1993).
The monograph presents a unified development of the origins, nature, methods and applications of Pitman’s measure of closeness (PMC) as a criterion in estimation. The PMC is based on the probabilities of the closeness of competing estimators to an unknown parameter. The text is written at the level of a graduate student in mathematical statistics. It is appropriate for a graduate-level course devoted to statistical inference and estimation techniques. The material of the text is covered in six chapters.
The introduction in Chapter 1 presents the motivation for exploring PMC. Chapter 2 contains discussions on the development of PMC. Chapter 3 discusses the operational aspects of adopting PMC as a criterion. The last three chapters present a unified development of the extensive theoretical and mathematical research on PMC. The text is properly referenced.
Reviewer: K.Alam (Clemson)


62F10 Point estimation
62-02 Research exposition (monographs, survey articles) pertaining to statistics
62-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to statistics