A Note on the Asymptotic Optimality of the Empirical Bayes Distribution Function
Benjamin Zehnwirth · The Annals of Statistics · 1981
This paper establishes the asymptotic optimality (in the sense of Robbins) of the empirical Bayes distribution function created from the Bayes rule relative to the Dirichlet process prior with unknown parameter $\alpha(.)$. It will follow that the same result applies to the estimation of the mean of a distribution function.