A new wavelet estimator of multivariate copula densities based on Sklar's theorem, with optimal strong uniform convergence rate

被引：0

作者：

Swanepoel, Jan ^{[1
]}

Seck, Cheikh Tidiane ^{[2
]}

Mamane, Salha ^{[3
]}

机构：

[1] North West Univ, Unit Data Sci & Comp, Potchefstroom, South Africa

[2] Alioune Diop Univ, Dept Math, Bambey, Senegal

[3] Univ Witwatersrand, Sch Stat & Actuarial Sci, Johannesburg, South Africa

来源：

SOUTH AFRICAN STATISTICAL JOURNAL | 2024年 / 58卷 / 02期

关键词：

Convergence rate; Copula; Nonparametric estimation; Wavelet; KERNEL ESTIMATION;

D O I：

10.37920/sasj.2024.58.2.2

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, we propose a natural wavelet estimator of multivariate copula densities as a ratio of the linear wavelet estimator of the underlying joint population density function and the product of the linear wavelet estimators of the corresponding marginal density functions. It is proven that the new estimator attains the optimal almost sure convergence rate over Besov balls for the supremum norm whenever the resolution level is suitably chosen.

引用

页码：99 / 108

页数：10

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