Accession Number : AD0660216

Title :   ON THE ADMISSIBILITY OF FORMAL BAYES ESTIMATORS.

Descriptive Note : Technical rept.,

Corporate Author : STANFORD UNIV CALIF DEPT OF STATISTICS

Personal Author(s) : Zidek,James Victor

Report Date : 21 SEP 1967

Pagination or Media Count : 99

Abstract : This work is concerned with the admissibility of formal Bayes estimators. Loss is assumed to be squared error. Positive results concern the case where the underlying distribution is known up to a single unknown parameter which is assumed to lie in a possibly infinite subinterval of the real line. Sufficient conditions are given for the almost admissibility, with respect to a prior measure pi, of formal Bayes estimators (of real functions of that parameter) obtained from pi. These conditions are reasonably explicit and give some new results in examples involving a member of the one parameter exponential family and the case of a single unknown location parameter. Two negative results are obtained. Both involve distributions (the normal and the exponential) with unknown location and scale parameters. It is shown that certain best affine invariant estimators are inadmissible. As an aid in obtaining one of these results, a representation, under fairly general conditions, of Bayes invariant procedures, in terms of Haar measure, is obtained. (Author)

Descriptors :   (*STATISTICAL ANALYSIS, DECISION THEORY), PROBABILITY, THESES, EXPONENTIAL FUNCTIONS, INVARIANCE, TOPOLOGY, TRANSFORMATIONS(MATHEMATICS), RANDOM VARIABLES, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE