On a Conjecture Concerning Least Favorable Configurations in Certain Two-Stage Selection Procedures

摘要

Given k normal populations with unknown means and a common known (or unknown) variance a two-stage procedure P sub 1 with screening in the first stage to find the population with the largest mean is under concern. It was proposed and studied previously by cohen (1959), Alam (1970), Tamhane and Bechhofer (1977, 1979) and Gupta and Miescke (1979). But up to now a conjecture concerning least favorable parameter configurations in an indifference zone approach remained unproved for k > or = 3. In this paper we give a non-standard proof of the conjecture in case of k = 3 for P sub 1 which (under minor changes) works also for a simplified version P sub 2. Besides, the point is exposed where another (more intuitive) method of proof fails to work. (Author)