Publication: Asymptotic properties of the Bernstein density copula for dependent data
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2008-07
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Abstract
Copulas are extensively used for dependence modeling. In many cases the data does
not reveal how the dependence can be modeled using a particular parametric copula.
Nonparametric copulas do not share this problem since they are entirely data based.
This paper proposes nonparametric estimation of the density copula for α-mixing data
using Bernstein polynomials. We study the asymptotic properties of the Bernstein
density copula, i.e., we provide the exact asymptotic bias and variance, we establish
the uniform strong consistency and the asymptotic normality.
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Nonparametric estimation, Copula, Bernstein polynomial, α-mixing, Asymptotic properties, Boundary bias