Some properties of the risk set in multiple decision problems (Q802230)

Some properties of the risk set of a decision problem with n-action, m- sample and 2-parameter are considered. It is shown that the number of vertices of the risk set is equal to \(mn\)-(t\({}_ 1+t_ 2)\), and that the number of essentially nonrandomized decision rules (defined in Section 1) in the minimal complete class is equal to \(m(n\)-1)\(+1\)-t\({}_ 1\), where \(t_ 1\) and \(t_ 2\) are defined in Section 2. Also, a procedure is given for getting all nonrandomized decision rules in the minimal complete class.