Classical ranking-and-selection (R&S) procedures cannot be applied directly to select the best decision in the presence of distributional ambiguity. In this paper we propose a robust selection-of-the-best (RSB) formulation which compares decisions based on their worst-case performances over a finite set of possible distributions and selects the decision with the best worst-case performance. To solve the RSB problems, we design two-layer R&S procedures, either two-stage or fully sequential, under the indifference-zone formulation. The procedure identifies the worst-case distribution in the first stage and the best decision in the second. We prove the statistical validity of these procedures and test their performances numerically.
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