Least Favorable Configuration When Ties are Broken

Abstract

The problem of selecting the t “best” populations from a set of k populations is considered where the observations (possibly already condensed) are of independent random variables Y_i , for i = 1, …, k, with distribution functions F(y; θ_i), which are nonincreasing in the θ _i for all y. The selection process is based on the values of the Y ₁, …, Y_k (ties being broken by randomization), and a theorem is proved which enables us to decide on a “least favorable configuration” for the θ _i values.