PARTIALLY BAYES ESTIMATES.
FLORIDA STATE UNIV TALLAHASSEE DEPT OF STATISTICS
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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 makers prior knowledge is reflected in his willingness to specify a subset, Lambdacalled 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.
- Statistics and Probability