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

Let X and Y be two independent continuous random variables. Three techniques to obtain confidence intervals for @r=Pr{Y>X} are discussed in a partially parametric framework. One method relies on the asymptotic normality of an estimator for @r; 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.

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