Estimating the density of a copula function

Abstract

This paper deals with estimation of the density of a copula function as well as with that of the Radon-Nikodym derivative of a bivariate distribution function with respect to the product of its marginal distribution functions. Strong uniform consistency and asymptotic normality of kernel-type estimators are proved under various conditions on the bandwidth and on the smoothness of the kernel. As an application, the estimation of Neyman-Pearson curves in the testing of independence problem is discussed.