ADMISSIBILITY OF THE BEST INVARIANT ESTIMATOR OF A DISCRETE DISTRIBUTION FUNCTION

We consider the problem of invariant estimation of a discrete distribu tion function F under the Cramer-von Mises loss. It is proved that the best invariant estimator is admissible. This extends a result of Brow n (1988) and settles an open question (Brown (1988)). The idea used in the proof of admissibility is a new refinement of the standard Bayes argument, which is different from the step-wise Bayes approach and Bly th's (1951) Lemma.