  In this paper, we investigate the almost sure convergence, in supremum norm,
of the rank-based linear wavelet estimator for a multivariate copula density.
Based on empirical process tools, we prove a uniform limit law for the
deviation, from its expectation, of an oracle estimator (obtained for known
margins), from which we derive the exact convergence rate of the rank-based
linear estimator. This rate reveals to be optimal in a minimax sense over Besov
balls for the supremum norm loss, whenever the resolution level is suitably
chosen.
