On a Necessary and Sufficient Condition for Admissibility of Estimators When Strictly Convex Loss is Used

Abstract

1. Introduction. In this paper we consider a necessary and sufficient condition for the admissibility of estimators when strictly convex loss is used. The result is stated as Theorem 1. The sufficiency of the condition is obvious and has served as the basis of admissibility proofs in [1], [6], [11], [3], and [2]. The necessity of such a method of proof is relatively deep. The author claims no practical use of Theorem 1. He has been moved primarily by curiosity about the necessity part of the theorem together with a desire to strengthen the tools of decision theory. The results of this paper depend on Farrell [5] to which one can refer for definitions of some common terms like Bayes if these are not clear.