For the problem of empirical Bayes classification into two known probability distributions on a finite outcome space, an essentially complete class of procedures is determined. This class is proven to be minimal essentially complete if there are only two possible outcomes.
"Complete Class Theorems for the Simplest Empirical Bayes Decision Problems." Ann. Statist. 5 (1) 164 - 171, January, 1977. https://doi.org/10.1214/aos/1176343749