Partially parametric interval estimation of Pr{Y>X}Pr{Y>X}

Let X and Y   be two independent continuous random variables. Three techniques to obtain confidence intervals for ρ=Pr{Y>X}ρ=Pr{Y>X} are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for ρρ; the remaining methods involve empirical likelihood and combine it with maximum likelihood estimation and with full parametric likelihood, respectively. Finite-sample accuracy of the confidence intervals is assessed through a simulation study. An illustration is given using a data set on the detection of carriers of Duchenne Muscular Dystrophy.