Summary
Let the random variableX be normal distributed with known varianceσ 2>0. It is supposed that the unknown meanθ is an element of a bounded intervalΘ. The problem of estimatingθ under the loss functionl p (θ, d)=|θ-d| p p≥2 is considered. In case the length of the intervalθ is sufficiently small the minimax estimator and theΓ(β, τ)-minimax estimator, whereΓ(β, τ) represents special vague prior information, are given.
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Bischoff, W., Fieger, W. Minimax estimators andΓ-minimax estimators for a bounded normal mean under the lossl p (θ, d)=|θ-d|p . Metrika 39, 185–197 (1992). https://doi.org/10.1007/BF02614000
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DOI: https://doi.org/10.1007/BF02614000