Nonparametric estimation of P(X < Y) using kernel methods

摘要

In this paper we consider point and interval estimation of P(X < Y). We used the kernel density estimators of the densities of the random variables X and Y, assumed independent. The resulting statistic is found to be similar in many ways to the Mann-Whitney statistic, however it assigns smooth continuous scores to the pairs of the observations rather than the zero or one scores of the Mann-Whitney statistic. A simulation study is conducted to investigate and compare the performance of the estimator based on this statistic and the Mann-Whitney estimator. Bootstrap confidence intervals based on the two statistics are investigated and compared.