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

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  • Brown, Lawrence D.

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.

Suggested Citation

  • Brown, Lawrence D., 1979. "Counterexample--An inadmissible estimator which is generalized bayes for a prior with "light" tails," Journal of Multivariate Analysis, Elsevier, vol. 9(2), pages 332-336, June.
    • Handle: RePEc:eee:jmvana:v:9:y:1979:i:2:p:332-336
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