Bernstein estimator for conditional copulas

The use of Bernstein polynomials in smooth nonparametric estimation of copulas has been well established in recent years. Their good properties in terms of bias and variance are well known. In this note we generalize some of the asymptotic theory to conditional copulas, that is where the dependence structure between the variables changes with a value of a random covariate. We obtain asymptotic representations and asymptotic normality for a conditional copula.