Institute of Mathematical Statistics Lecture Notes - Monograph Series

Estimation in restricted parameter spaces: a review

Eric Marchand and William E. Strawderman

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Abstract

In this review of estimation problems in restricted parameter spaces, we focus through a series of illustrations on a number of methods that have proven to be successful. These methods relate to the decision-theoretic aspects of admissibility and minimaxity, as well as to the determination of dominating estimators of inadmissible procedures obtained for instance from the criteria of unbiasedness, maximum likelihood, or minimum risk equivariance. Finally, we accompany the presentation of these methods with various related historical developments.

Chapter information

Source
Anirban DasGupta, ed., A Festschrift for Herman Rubin (Beachwood, Ohio, USA: Institute of Mathematical Statistics, 2004), 21-44

Dates
First available in Project Euclid: 28 November 2007

Permanent link to this document
https://projecteuclid.org/euclid.lnms/1196285377

Digital Object Identifier
doi:10.1214/lnms/1196285377

Mathematical Reviews number (MathSciNet)
MR2126884

Zentralblatt MATH identifier
1268.62030

Subjects
Primary: 62-02: Research exposition (monographs, survey articles) 62C99: None of the above, but in this section 62C15: Admissibility 62C20: Minimax procedures 62C10: Bayesian problems; characterization of Bayes procedures 62F10: Point estimation 62F30: Inference under constraints

Keywords
restricted parameter spaces minimaxity admissibility dominating procedures maximum likelihood estimation

Rights
Copyright © 2004, Institute of Mathematical Statistics

Citation

Marchand, Eric; Strawderman, William E. Estimation in restricted parameter spaces: a review. A Festschrift for Herman Rubin, 21--44, Institute of Mathematical Statistics, Beachwood, Ohio, USA, 2004. doi:10.1214/lnms/1196285377. https://projecteuclid.org/euclid.lnms/1196285377


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