Statistical decisions under ambiguity |
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Authors: | Jörg Stoye |
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Institution: | 1.Department of Economics,New York University,New York,USA;2.Department of Economics,Cornell University,Ithaca,USA |
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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 c-independence 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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Keywords: | |
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