A new wavelet estimator of multivariate copula densities based on Sklar's theorem, with optimal strong uniform convergence rate

Abstract

In this paper, we propose a natural wavelet estimator of multivariate copula densities as a ratio of the linear wavelet estimator of the underlying joint population density function and the product of the linearwavelet estimators of the corresponding marginal density functions. It is proven that the new estimator attains the optimal almost sure convergence rate over Besov balls for the supremum norm whenever the resolution level is suitably chosen.