Procedures for improving the mle for ordered binomial parameters

The problem is that of estimating the probabilities of m independent binomial random variables when their probabilities are known to be nondecreasing and the loss function is squared error. In the cases where the m.l.e. is inadmissible (essentially when the total number of trials is 7 or more) we present a method for modifying the m.l.e. to get a better estimator. The method requires a series of changes. At each step we alter the action taken by the m.l.e. on each of three, appropriately chosen, points in the sample space.