ESTIMATING P(X-GREATER-THAN-Y) IN EXPONENTIAL MODEL REVISITED

The problem of estimating theta = P {X > Y} in the exponential model i s reconsidered. The performance of the nonparametric unbiased estimato r <(theta)over tilde> based on U-statistic is examined against the Uni formly Minimum Variance Unbiased Estimator <(theta)over cap>, proposed in the literature. Among other desirable properties, it is demonstrat ed that the estimator <(theta)over tilde>, its variance V(<(theta)over tilde>, and the U-statistic based unbiased estimator (V) over cap(<(t heta)over tilde>) of the variance V(<(theta)over tilde>) have simple e xpressions, easily amenable to recursive estimation. It is further sho wn that (V) over cap(<(theta)over tilde>) greater than or equal to 0. Our numerical study indicates that generally we should be better off b y using <(theta)over tilde> against possible outliers in the model.