Partially parametric interval estimation of Pr(Y>X)

Let X andY be two independent continuous random variables. Three techniques to obtain confidence intervals for \rho=PrY >X are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for \rho; 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.