Estimation of irregular probability densities

Abstract

This paper deals with nonparametric estimation of an unknown density function which possibly is discontinuous or non-differentiable in an unknown finite number of points. Estimation of such irregular densities is accomplished by viewing the problem as a regression problem and applying recent techniques for estimation of irregular regression curves. Moreover, the method can deal with estimation of densities that have an irregularity at the endpoint(s) of their support. A simulation study compares the performance of the proposed method with those of other methods available in the literature. A further illustration on real data is provided.