ADMISSIBILITY AND MINIMAXITY OF THE UMVU ESTIMATOR OF P(X-LESS-THAN-Y)

Suppose that X(1),...,X(m) are i.i.d. from a continuous distribution f unction F and Y-1,...,Y-n are i.i.d. from a continuous distribution fu nction G; X's and Y's are independent. A minimum variance unbiased est imator of P(X < Y) is the Mann-Whitney statistic. We show that the Man n-Whitney statistic is admissible under a class of weighted squared er ror losses and is minimax under a proper weighted squared error loss.