Minimax estimation method for the optimum decomposition of a sample space based on prior information
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Existences and expressions of minimax estimators based on prior information for the optimum decomposition of a given sample space are studied in a unifying way such that answers can be easily obtained by applying the theorems given in this paper to various statistical problems—optimum selection regions, tolerance regions, prediction regions, optimum stratifications and so on.
Further, ε-approximations to those estimators are given by choosing a finite family of probability measures from the infinite family of them under consideration in such a way that the former may be considered to be a sufficiently good approximation to the latter in the sense of risk function.
Besides, those estimators are proved to be consistent in the sense that the risk decreases to zero as the amount of prior information increases infinitely.
KeywordsProbability Measure Prior Information Risk Function Decision Function Weak Topology
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