With respect to a general quadratic loss function, the Bayes rule for the mean of a probability distribution of unknown form is obtained, in the class of linear functions of the sample. The associated Bayes risk is also obtained. A number of recent results in the literature are shown to be direct corollaries of this result, and applications are given for the empirical distribution function of the sample.
"A Note on Some Bayesian Nonparametric Estimates." Ann. Statist. 3 (3) 736 - 740, May, 1975. https://doi.org/10.1214/aos/1176343138