  We propose two classes of nonparametric point estimators of $\theta=P(X<Y)$
in the case where $(X,Y)$ are paired, possibly dependent, absolutely continuous
random variables. The proposed estimators are based on nonparametric estimators
of the joint density of $(X,Y)$ and the distribution function of $Z=Y - X$. We
explore the use of several density and distribution function estimators and
characterise the convergence of the resulting estimators of $\theta$. We
consider the use of bootstrap methods to obtain confidence intervals. The
performance of these estimators is illustrated using simulated and real data.
These examples show that not accounting for pairing and dependence may lead to
erroneous conclusions about the relationship between $X$ and $Y$.
