Statistical decisions under ambiguity

Authors: Jörg Stoye

Publish Date: 2010/09/05

Volume: 70, Issue: 2, Pages: 129-148

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Abstract

This article provides unified axiomatic foundations for the most common optimality criteria in statistical decision theory It considers a decision maker who faces a number of possible models of the world possibly corresponding to true parameter values Every model generates objective probabilities and von Neumann–Morgenstern expected utility applies where these obtain but no probabilities of models are given This is the classic problem captured by Wald’s Statistical decision functions 1950 device of risk functions In an Anscombe–Aumann environment I characterize Bayesianism as a backdrop the statistical minimax principle the Hurwicz criterion minimax regret and the “Pareto” preference ordering that rationalizes admissibility Two interesting findings are that cindependence is not crucial in characterizing the minimax principle and that the axiom which picks minimax regret over maximin utility is von Neumann–Morgenstern independence

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