Date of this Version
The Annals of Statistics
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.
estimation, admissibility, (nonlinear) differential inequalities, generalized Bayes estimators, estimation location parameters, estimating Poisson means, estimating the largest mean, estimating a normal variance (mean unknown).
Brown, L. D. (1979). A Heuristic Method for Determining Admissibility of Estimators--With Applications. The Annals of Statistics, 7 (5), 960-994. http://dx.doi.org/10.1214/aos/1176344782
Date Posted: 27 November 2017
This document has been peer reviewed.