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On various criteria of optimality in probabilistic decision-making. (English) Zbl 0776.90006
Summary: There are two possibilities of how to define the optimality of a decision function — with respect to a given set of distributions — in “local” and “global” senses, applying the minimax rule. But an optimal decision function in any of these senses need not be the optimal one for any distributions in this set. It is shown, using linear programming methods, how to find out whether the global minimax decision function is optimal or not. A suitable representation of the decision function is found — in the latter case — on the base of a barycenter concept.

91B06 Decision theory
62C20 Minimax procedures in statistical decision theory
90C05 Linear programming
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