Nonparametric density estimation of continuous part of a mixed measure

Abstract

We consider a pair of random variables(X,Y) whose probability measure is the sum of an absolutely continuous measure, a discrete measure and a finite number of absolutely continuous measures on several lines(1). An asymptotically unbiased and consistent estimate, at all points, of the density of the continuous part is given as well as its rate of convergence. We also estimate the amplitude of the discrete measure and the densities on several lines.