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.

翻译：本文研究基于秩的多元连接函数密度线性小波估计量在一致范数下的几乎必然收敛性。利用经验过程工具，我们证明了预言估计量（基于已知边缘分布获得）与其期望之偏差的一致极限定律，并由此推导出基于秩的线性估计量的精确收敛速率。当分辨率水平适当选择时，该速率在贝索夫球上关于一致范数损失在极小极大意义下达到最优。