Asymptotically optimal empirical Bayes squared error loss estimation procedures are developed for three families of continuous distributions, uniform $(0, \theta), \theta > 0,$ uniform $\lbrack \theta, \theta + 1), \theta$ arbitrary, and a location parameter family of gamma distributions. The approach taken is to estimate the Bayes estimator directly. However, for the $\lbrack \theta, \theta + 1)$ case, it is shown that the indirect approach of applying the Bayes estimator, versus an almost sure weakly convergent estimator of the prior, also yields an asymptotically optimal procedure.
"Solutions to Empirical Bayes Squared Error Loss Estimation Problems." Ann. Statist. 6 (4) 846 - 853, July, 1978. https://doi.org/10.1214/aos/1176344258