Some properties of the risk set in multiple decision problems

Abstract

Some properties of the risk set of a decision problem withn-action,m-sample and 2-parameter are considered. It is shown that the number of vertices of the risk set is equal tomn−(t1+t2), and that the number of essentially nonrandomized decision rules (defined in Section 1) in the minimal complete class is equal tom(n−1)+1−t1, wheret1 andt2 are defined in Section 2. Also, a procedure is given for getting all nonrandomized decision rules in the minimal complete class.