Statistics Papers

Document Type

Journal Article

Date of this Version

1979

Publication Source

The Annals of Statistics

Volume

7

Issue

5

Start Page

960

Last Page

994

DOI

10.1214/aos/1176344782

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.

Comments

At the time of publication, author Lawrence Brown was affiliated with Rutgers University. Currently, he is a faculty member at the Statistics Department at the University of Pennsylvania.

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).

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Date Posted: 27 November 2017

This document has been peer reviewed.