The Annals of Statistics

A Heuristic Method for Determining Admissibility of Estimators--With Applications

Lawrence D. Brown

Full-text: Open access

Abstract

Questions of admissibility of statistical estimators are reduced to considerations involving differential inequalities. The coefficients of these inequalities involve moments of the underlying distributions; and so are, in principle, not difficult to derive. The methods are "heuristic" because it is necessary to verify on an ad-hoc basis that error terms are small. Some conditions on the structure of the problem are given which we believe will guarantee that these error terms are small. Several different statistical estimation problems are discussed. Each problem is transformed (if necessary) so as to meet the above mentioned structure conditions. Then the heuristic method is applied in order to generate conjectures concerning the admissibility of certain generalized Bayes procedures in these problems.

Article information

Source
Ann. Statist., Volume 7, Number 5 (1979), 960-994.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344782

Digital Object Identifier
doi:10.1214/aos/1176344782

Mathematical Reviews number (MathSciNet)
MR536501

Zentralblatt MATH identifier
0414.62011

JSTOR
links.jstor.org

Subjects
Primary: 62C15: Admissibility
Secondary: 62F10: Point estimation 65M99: None of the above, but in this section 65P05 62H99: None of the above, but in this section 62C10: Bayesian problems; characterization of Bayes procedures

Keywords
Estimation admissibility (nonlinear) differential inequalities generalized Bayes estimators estimation location parameters estimating Poisson means estimating the largest mean estimating a normal variance (mean unknown).

Citation

Brown, Lawrence D. A Heuristic Method for Determining Admissibility of Estimators--With Applications. Ann. Statist. 7 (1979), no. 5, 960--994. doi:10.1214/aos/1176344782. https://projecteuclid.org/euclid.aos/1176344782


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