van Eeden, Constance Restricted parameter space estimation problems. Admissibility and minimaxity properties. (English) Zbl 1160.62018 Lecture Notes in Statistics 188. New York, NY: Springer (ISBN 0-387-33747-4/pbk). x, 167 p. (2006). The book under review is addressed to the audience interested in the subject of admissibility and minimaxity in restricted-parameter-space estimation. It covers results from the time when the subject began to be studied (early 1950s) to the middle of 2004, depicts relationships between various results, and points out open problems. The topic of hypothesis testing is not touched here. The introduction, which gives some history and examples, is followed by seven chapters. In Chapter 2, a general statement of the problem is offered. Chapters 3 and 4 contain, respectively, results on admissibility and minimaxity when there are no nuisance parameters. Results for the case where nuisance parameters are present are the topic of Chapter 5, while Chapter 6 deals with results for linear models. Some other properties of restricted parameter space estimators, such as robustness to misspecification of the parameter space and unbiasedness, as well as relationships with Hu and Zidek’s weighted likelihood estimation, can be found in Chapter 7. Chapter 8 contains existence results for maximum likelihood estimators under order restrictions on the parameters, and some properties of these estimators (together with computational algorithms) are given. An extensive bibliography is provided. Reviewer: Joseph Melamed (Los Angeles) Cited in 48 Documents MSC: 62F10 Point estimation 62F30 Parametric inference under constraints 62C15 Admissibility in statistical decision theory 62C20 Minimax procedures in statistical decision theory 62-02 Research exposition (monographs, survey articles) pertaining to statistics PDFBibTeX XMLCite \textit{C. van Eeden}, Restricted parameter space estimation problems. Admissibility and minimaxity properties. New York, NY: Springer (2006; Zbl 1160.62018) Full Text: DOI