Admissibility in Statistical Problems Involving a Location or Scale Parameter

The purpose of this short paper is to point out how a slight modification of the formulation of the problem in Brown (1966) yields a variety of admissibility results for problems involving an unknown location or scale parameter. The results sketched, but not proved, include some applications of the analogous two parameter results in Brown and Fox (1974). The applications involve testing problems, estimation problems, and confidence set problems. We treat here only fixed sample size situations; although there also exist similar sequential applications. The proof is essentially that contained in Brown (1966).