Admissibility of the best invariant estimator of a discrete distribution function

We consider the problem of invariant estimation of a discrete distribution function F under the Cramer-von Mises loss. It is proved that the best invariant estimator is admissible. This extends a result of Brown (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 Blyth's (1951) Lemma.