A Note on the Estimation of Binomial Probabilities

I am concerned with the admissibility under quadratic loss of certain estimators of binomial probabilities.The minimum variance unbiased estimator is shown to be admissible for Pr(X = 0) and Pr(X = n), but it is inadmissible for Pr(X = k), where 0 < k < n.An example is given of an admissible maximum likelihood estimator (MLE). It is conjectured that the MLE is always admissible.