Journal of Data Science

Abstract: We propose two classes of nonparametric point estimators of θ = 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 distri bution function of Z = Y − X. We explore the use of several density and distribution function estimators and characterise the convergence of the re sulting estimators of θ. We consider the use of bootstrap methods to obtain confidence intervals. The performance of these estimators is illustrated us ing simulated and real data. These examples show that not accounting for pairing and dependence may lead to erroneous conclusions about the rela tionship between X and Y .