A nonparametric measure of the overlapping coefficient

Abstract

We examine the sampling behavior of a nonparametric estimator of the overlapping coefficient. The overlapping coefficient is a proposed measure of the discrepancy between two independent samples. Using Monte Carlo techniques, it is discovered that the sampling estimator of the overlapping coefficient using the naive kernel density estimator is biased. The bias of the kernel estimator of the overlapping coefficient increases as the similarity of the distributions from which the samples are obtained increases. Yet, the bias of the estimator in most cases is minimal. A bootstrap estimator of the sampling standard deviation of the nonparametric estimator of the overlapping coefficient was also examined. The behavior of the sampling estimator of the overlap suggest that the overlapping coefficient can best serve as a valuable check in investigation of differences detected between two distributions by standard statistical techniques.