Restricted Parameter Space Estimation Problems: Admissibility and Minimaxity Properties

Paperback | September 21, 2006

byConstance van Eeden

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This monograph contains a critical review of 50 years of results on questions of admissibility and minimaxity of estimators of parameters that are restricted to closed convex subsets of Rk . It presents results of approximately 300 mostly-published papers on the subject, and points out relationships between them as well as open problems. The book does not touch on the subject of testing hypotheses for such parameter spaces. It does give an overview of known algorithms for computing maximum likelihood estimators under order-restrictions. The book should be valuable as a reference for researchers and graduate students looking for what is known and unknown in the area of restricted parameter-space-estimation. It assumes a good knowledge of decision theory.

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This monograph contains a critical review of 50 years of results on questions of admissibility and minimaxity of estimators of parameters that are restricted to closed convex subsets of Rk . It presents results of approximately 300 mostly-published papers on the subject, and points out relationships between them as well as open problem...

From the Jacket

This monograph contains a critical review of 50 years of results on questions of admissibility and minimaxity of estimators of parameters that are restricted to closed convex subsets of Rk . It presents results of approximately 300 mostly-published papers on the subject, and points out relationships between them as well as open problem...

Format:PaperbackDimensions:178 pages, 9.25 × 6.1 × 0 inPublished:September 21, 2006Publisher:Springer New YorkLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0387337474

ISBN - 13:9780387337470

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Table of Contents

Introduction: Some History and Some Examples.- A Statement of the Problem, The Notation and Some Definitions.- (In)Admissibility and Dominators.- Minimax Estimators and their Admissibility.- Presence of Nuisance Parameters.- The Linear Model.- Other Properties.- Existence of the Mles and Algorithms to Compute Them.

Editorial Reviews

From the reviews:"This book is well written and well organized. The material is motivated with examples...[t]he monograph could be used for PhD-level special topics class...,[and] students with a background in mathematical statisics would benefit from researching and presenting in detail the specific examples of interesting problems." (Mary Meyer, for Biometrics, December 2007)"This monograph contains a critical review of 50 years of research on estimators in convex, restricted k-dimensional parameter spaces . . The bibliography contains about 300 items, mostly published papers and books on the subject. . Questions about the existence and properties of maximum likelihood estimators are discussed, and some algorithms for computing them are presented. . The book represents a valuable guide to the literature in the area of restricted-space estimation and to what is known and not known in this area." (Jon Stene, Mathematical Reviews, Issue 2008 h)"The literature on the estimation of parameters subject to order restrictions is not well documented in any book until now, and the author should be congratulated for writing an important book that fills the gap. The book provides an excellent summary of several major results available in the literature on the estimation of parameters subject to order restrictions. . the 16-page bibliography, covering over 250 publications, serves as an excellent reference for researchers interested in this field." (Shyamal D. Peddada, Journal of the American Statistical Association, Vol. 103 (482), June, 2008)"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 . to the middle of 2004, depicts relationships between various results, and points out open problems. . The introduction, which gives some history and examples, is followed by seven chapters. . An extensive bibliography is provided." (Joseph Melamed, Zentralblatt MATH, Vol. 1160, 2009)