Counterexample--An inadmissible estimator which is generalized bayes for a prior with "light" tails

Lawrence D. Brown

Journal of Multivariate Analysis, 1979, vol. 9, issue 2, 332-336

Abstract: Previous work on the problem of estimating a univariate normal mean under squared error loss suggests that an estimator should be admissible if and only if it is generalized Bayes for a prior measure, F, whose tail is "light" in the sense that [integral operator]1[infinity] f*-1(x) DX = [infinity] = [integral operator]-[infinity]-1 f*-1(x) dx, where f* denotes the convolution of F with the normal density. (There is also a precise multivariate analog for this condition.) We provide a counterexample which shows that this suggestion is false unless some further regularity conditions are imposed on F.

Keywords: estimating; a; normal; mean; generalized; Bayes; estimators (search for similar items in EconPapers)
Date: 1979
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