Abstract
an arbitrary procedure from each Dk? The answer turns out to be no in a large class of such decision problems which we consider here. This means that by planning our whole sequence of decision procedures in advance we are able to do better on an average than if we were to make each decision as it arises. The present paper is devoted to the problem of prescribing rules which tell how the single-stage decision procedures dk should interlock with one another so as to give a minimal complete class of decision procedures for the multistage statistical decision problem. This problem is similar to the classical sequential decision problems which do not fix in advance the number of stages. In many respects the problem formulated here is simpler than the classical sequential decision problem, and sharper results are obtained-e.g., minimal complete classes of
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