Controlling Risks under Different Loss Functions: The Compromise Decision Problem
The Annals of Statistics · 1988 · Volume 16 · Issue 4
Abstract
Controlling Bayes and/or minimax risks under possibly different loss functions is formulated as a problem faced by two or more statisticians who must compromise and agree on the use of a single decision procedure. The theory characterizing solutions to Bayes compromise problems and minimax-Bayes compromise problems is presented. In a Bayes compromise problem, Bayes risks under different prior distributions and/or loss functions are minimized simultaneously. In a minimax-Bayes compromise problem, a Bayes risk under some loss function for a given prior distribution and a maximum risk under a possibly different loss function are minimized simultaneously.
Keywords
62C05, 62C25, Bayes inference, group decision analysis, minimax, multiple objective decision analysis
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