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

Cheikh Tidiane  Seck; Salha Mamane

doi:10.37920/sasj.2024.58.1.3

Cheikh Tidiane Seck Department of Mathematics, Alioune Diop University, Bambey, Senegal
Salha Mamane School of Statistics and Actuarial Science, University of the Witwatersrand, Johannesburg, South Africa

DOI: https://doi.org/10.37920/sasj.2024.58.1.3

Keywords: Almost sure uniformconvergence rates, Copula density, Nonparametric estimation, Wavelet methods

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.

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