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

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.