PARTIALLY BAYES ESTIMATES.
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.
Document Details
- Document Type
- Technical Report
- Publication Date
- Jan 01, 1969
- Accession Number
- AD0685595
Entities
People
- Daniel L. Solomon
Organizations
- Florida State University