Kostenoptimale Prüfpläne bei einem Problem mit drei möglichen Entscheidungen (Q1057612)

After having sampled pairs \((x_ 1,x_ 2)\) from a universe \(A\times B\) with three possible examination results, \(x_ 1\) better than \(x_ 2\), \(x_ 1\) worse than \(x_ 2\), and \(x_ 1,x_ 2\) indifferent, one has to decide if the first universe A is better or worse than or indifferent to the second universe B. The strategy space is the set of all \((n,c_ 1,c_ 2)\) where n is the sample size and the decisions are (X is the number of pairs in the sample with \(x_ 1\) better than \(x_ 2):\) A worse than B, if \(X\leq c_ 1\), A indifferent to B, if \(c_ 1<X\leq c_ 2\), and A better than B, if \(X>c_ 2\). The cost model is composed by sampling costs and final decision costs, the optimality criterion is the minimax-regret-principle. Theorems on existence, necessary conditions and structure of optimal strategies are proven, such as the possible restriction to symmetric strategies (i.e., \(c_ 2=n-c_ 1-1)\). A method for determining an optimal strategy is described.