ADMISSIBILITY RESULTS IN LOSS ESTIMATION

In this paper we consider the problem of estimating the loss of point estimators and study admissibility of such estimators of loss. We adap t and extend the ''unified admissibility proof'' idea of Brown and Hwa ng to this problem. We first present the result in the Gaussian setup. We then generaIize the procedure to general exponential family distri butions and apply it to the Poisson distribution. The result for the g amma distribution is also stated. The role played by the ''polydisc tr ansform'' (cf. Johnstone and MacGibbon) in making explicit the relatio nship between the Gaussian and Poisson cases is discussed.