A point estimation of P(X < Y) was considered. A nonparametric estimator for P(X < Y) was developed using the kernel density estimator of the joint distribution of X and Y, may be dependent. The resulting estimator was found to be similar to the estimator based on the sign statistic, however it assigns smooth continuous scores to each pair of the observations rather than the zero or one scores of the sign statistic. The asymptotic equivalence of the sign statistic and the proposed estimator is shown and a simulation study is conducted to investigate the performance of the proposed estimator. Results indicate that the estimator has a good overall performance.
Eidous, Omar M. and Baklizi, Ayman
"Kernel-Based Estimation of P(X less than Y)With Paired Data,"
Journal of Modern Applied Statistical Methods: Vol. 3
, Article 14.
Available at: http://digitalcommons.wayne.edu/jmasm/vol3/iss1/14