A Note on the Lower Bound for the P(CS) of Gupta's Subset Selection Procedure.
Robert E. Bechhofer, Thomas J. Santner · Defense Technical Information Center (DTIC) · 1979
The lower bound on the specified P* for the Gupta procedure for selecting a subset containing the best of k populations, and for the Gupta-Sobel procedure for selecting a subset containing all populations at least as good as a control population is studied via impartial 'no data' minimax decision rules. Gibbons, Olkin, and Sobel (1977) state that a theoretical lower bound is 1/2(k) for both problems. Our analysis shows (a) that 1/k is the correct lower bound for the first problem, and (b) that 1/2(k) is the correct lower bound for the second problem provided that a particular loss function is adopted. Other (reasonable) choices of loss function lead to different lower bounds for the second problem. (Author)