Summary
It is desired to estimate a parameter
with the loss function of the formL(θ, a)=W(‖θ−a‖), where
is convex, differentiable, and non-decreasing. With this structure a characterization of Bayes estimators is given. Also it is noted that if the sample space,
, for the observation,X, is a complete separable metric space then a Bayes estimator exists.
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Umbach, D. Bayes estimation with spherically symmetric, convex loss. Ann Inst Stat Math 33, 81–90 (1981). https://doi.org/10.1007/BF02480921
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DOI: https://doi.org/10.1007/BF02480921