A note on the asymptotic behavior of the Bernstein estimator of the copula density

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• 作者：Paul Janssen ; Jan Swanepoel ; No毛l Veraverbeke
• 关键词：primary ; 62G05 ; 62G07 ; secondary ; 62G20
• 刊名：Journal of Multivariate Analysis
• 出版年：February, 2014
• 年：2014
• 卷：124
• 期：Complete
• 页码：480-487
• 全文大小：379 K

文摘

Copulas and their corresponding densities are functions of a multivariate joint distribution and the one-dimensional marginals. Bernstein estimators have been used as smooth nonparametric estimators for copulas and copula densities. The purpose of this note is to study the asymptotic distributional behavior of the Bernstein estimator of a copula density. Compared to the existing results, our general theorem does not assume known marginals. This makes our theorem applicable for real data.