Publication: Bernstein estimator for unbounded density copula
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2011-10
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Abstract
We study the asymptotic properties of the Bernstein estimator for unbounded density copula
functions. We show that the estimator converges to infinity at the corner. We establish its relative
convergence when the copula is unbounded and we provide the uniform strong consistency of the
estimator on every compact in the interior region. We also check the finite simple performance of the
estimator via an extensive simulation study and we compare it with other well known nonparametric
methods. Finally, we consider an empirical application where the asymmetric dependence between
international equity markets (US, Canada, UK, and France) is re-examined.
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Unbounded copula, Nonparametric estimation, Bernstein polynomial, Asymptotic properties, Uniform strong consistency, Relative convergence, Boundary bias