SOME RESULTS IN THE DECISION THEORY OF ONE-PARAMETER MULTIVARIATE POLYA TYPE DISTRIBUTIONS

摘要

Karlin has recently called attention to the fact that virtually all families of distributions considered in parametric decision problems fall into a class, which he calls Polya type, whose salient feature is a certain "sign-change diminishing" property enabling one to get a grip on the decision theory for these problems, that is to characterize the Bayes procedures and essentially complete classes and, often, even to find the admissible procedures. In this paper, we obtain multi-dimensional (or multivariate) analogues of the results on essential completeness given by Karlin in the two-action case, and by Karlin and Rubin in the several-action case.