AN ESSENTIALLY COMPLETE CLASS OF TWO-STAGE SELECTION PROCEDURES WITH SCREENING AT THE FIRST STAGE
Shanti S. Gupta, Klaus J. Miescke · Statistics & Risk Modeling · 1983
Let (pi sub 1),...,(pi sub k) be given populations associated with unknown real parameters (theta sub 1),...,(theta sub k). The goal is to find a population with a sufficiently large parameter in two stages with screening out inferior populations at the first stage. Both, the control and the non-control situations are considered simultaneously. Let sub I denote the class of permutation invariant randomized procedures (thi, psi, gamma), where at Stage 1, thi and psi decide how many populations and then which ones, respectively, are selected, and where at Stage 2, after additional samples have been drawn from the selected populations, gamma makes the final decision. Let psi and gamma denote the natural decisions, i.e. which are associated with the largest sufficient statistics. Under the assumption of a common discrete or continuous type strongly unimodal exponential family it is shown that with respect to every reasonable loss function, procedures of the type (thi, psi, gamma) form an essentially complete class within d sub I. (Author)