Accession Number : AD0685595

Title :   PARTIALLY BAYES ESTIMATES.

Descriptive Note : Technical rept.,

Corporate Author : FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS

Personal Author(s) : Solomon,Daniel L.

Report Date : JAN 1969

Pagination or Media Count : 90

Abstract : Statistical decision problems are considered in which the decision maker is assumed to have prior information but cannot completely specify a prior distribution. The decision maker's prior knowledge is reflected in his willingness to specify a subset, Lambda*(called an incompleteness specification) of the class of all prior distribution lambda. He is then recommended to select the decision rule to minimize the maximum over distributions in Lambda* of the Bayes risk. Such a rule is called partially Bayes with respect to Lambda*, and reduces to the Bayes rule with respect to lambda if Lambda* = (lambda) and the minimax rule if Lambda* = Lambda. The particular problems of estimation of a general mean and a Normal variance are considered in detail. Examples of the determination of optimal sample size and incompleteness specification are given for the two problems.

Descriptors :   (*STATISTICAL ANALYSIS, *DECISION THEORY), PROBABILITY, MINIMAX TECHNIQUE, STATISTICAL DISTRIBUTIONS, DECISION MAKING, GAME THEORY, MATHEMATICAL MODELS, THEOREMS

Subject Categories : Statistics and Probability

Distribution Statement : APPROVED FOR PUBLIC RELEASE