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

Authors
Journal
Journal of Multivariate Analysis
0047-259X
Publisher
Elsevier
Volume
124
Identifiers
DOI: 10.1016/j.jmva.2013.10.009
Keywords
  • Asymptotic Normality
  • Bernstein Estimator
  • Copula Density
Disciplines
  • Mathematics

Abstract

Abstract 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.

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