A simulation study of the efficiency of empirical Baye’s estimators of multiple correlated probability vectors

Empirical Bayes’ methods had been used by Brier, Zacks, and Marlow for estimating performance characteristic vectors of success probabilities. The problem is that of estimating k-dimensional success probabilities of dependent binomial random variables, which are highly correlated. The present study reinforces the results of the previous one by showing, via simulations, that the relative efficiency of the empirical Bayes estimators, compared to the Stein-type and to the maximum-likelihood ones, is very high. This holds even if the success proportions are based on a small number of trials. The authors study the case of equicorrelation structure with positive correlations.