In this paper we consider the problem of estimating the loss of point estimators and study admissibility of such estimators of loss. We adapt and extend the "unified admissibility proof" idea of Brown and Hwang to this problem. We first present the result in the Gaussian setup. We then generalize the procedure to general exponential family distributions and apply it to the Poisson distribution. The result for the gamma distribution is also stated. The role played by the "polydisc transform" (cf. Johnstone and MacGibbon) in making explicit the relationship between the Gaussian and Poisson cases is discussed.
"Admissibility Results in Loss Estimation." Ann. Statist. 21 (1) 378 - 390, March, 1993. https://doi.org/10.1214/aos/1176349031