Abstract: We study the problem of estimating the mean of a univariate normal population when the mean is known to be non-negative and loss is squared error. The MLE is superior to the UMVUE, but it is known that the MLE is itself inadmissible. A long unsolved problem is to find an explicit estimator which dominates the MLE. This paper is devoted to producing a class of such estimators. We believe, but have not proved, that some members of our class are admissible.
Key words and phrases: Minimaxity, squared error loss, location parameter.