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An extension of the usual model in statistical decision theory with applications to stochastic optimization problems

By E.J. Balder


By employing fundamental results from “geometric” functional analysis and the theory of multifunctions we formulate a general model for (nonsequential) statistical decision theory, which extends Wald's classical model. From central results that hold for the model we derive a general theorem on the existence of admissible nonrandomized Bayes rules. The generality of our model makes it also possible to apply these results to some stochastic optimization problems. In an appendix we deal with the question of sufficiency reduction

Topics: Wiskunde en Informatica, statistical decision theory, Bayes rule, measurable multifunctions, stochastic programming, sufficiency reduction
Year: 1980
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