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arXiv · 2303.05627

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

Cheikh Tidiane Seck·Salha Mamane
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Abstract

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.

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Cheikh Tidiane Seck, Salha Mamane. 2023-03-10. Strong uniform convergence rates of the linear wavelet estimator of a multivariate copula density. https://arxiv.org/abs/2303.05627

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