
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