Strong uniform convergence rates of the linear wavelet estimator of a multivariate copula density
| Autor: | Seck, Cheikh Tidiane, Mamane, Salha |
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| Rok vydání: | 2023 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | 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. Comment: 23 pages |
| Databáze: | arXiv |
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