Empirical Bayesian Multiple Comparisons with the Best

A parametric empirical Bayes procedure is proposed and studied to compare treatments simultaneously with the best. Minimum Bayes risk lower bounds are derived for an additive loss function, and their relationship with Bayesian simultaneous confidence lower bounds is given. For the proposed empirical Bayes procedure, the nominal confidence level both in Bayesian sense and in frequentist's sense is shown to be controlled asymptotically. For practical implementation, a measure of significance similar to f-value is suggested with an illustrative example.