On Simple Rules for the Compound Decision Problem

Summary The general non-sequential and sequential compound decision problem is considered. A rule is simple if it uses the ith observation only, in order to make the ith decision. It is shown that simple rules, the components of which are Bayes rules for the component problem, are Bayes rules also for the compound problem, and hence, under certain regularity conditions, are admissible compound rules. Nevertheless, a property (A), usually aimed at in the compound situation, cannot be achieved by any simple rule, except in trivial cases.