Admissibility Considerations in the Finite State Compound and Empirical Bayes Decision Problems*

Abstract

SummaryIn the compound decision problem the same decision problem. called the component decision problem, occurs repeatedly. Data from all repetitions are used to reach decisions concerning the parameter values in each component; such rules are called compound decision rules. The compound risk is the average risk across all component decisions. In the analogous empirical Bayes problem the parameters are taken to be independent and identically distributed with unknown distribution. This paper explores the relationship between compound risk admissibility and component risk admissibility in these problems. The definitions are general and the results are fairly obvious and proved for the finite parameter set component only.