A Rational Decision Criterion, the Iterated Minimax Regret Criterion

Abstract

We feel that a criterion for selecting optimal decision rules in a statistical decision problem should be selected rationally. Specifically, we would like a criterion to satisfy eight properties which we have given. It is known that none of the commonly used criteria satisfy these eight properties. We give sufficient conditions on the decision problem so that the iterated minimax regret criterion does satisfy all eight properties, and give examples to show that these sufficient conditions cannot be removed.