Strong uniform convergence rates of the linear wavelet estimator of a multivariate copula density

Abstract

In this paper, we investigate the almost sure convergence, in supremum norm, of the rank-based linear wavelet estimator for the multivariate copula density over Besov classes. Using empirical process tools, we establish a uniform limit law for the deviation of an oracle estimator (which assumes known margins) from its expectation. This enables us to derive strong convergence rates for the rank-based linear estimator.