Bernstein estimator for unbounded copula densities
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Taoufik Bouezmarni
Abstract
Copulas are widely used for modeling the dependence structure of multivariate data. Many methods for estimating the copula density functions are investigated. In this paper, we study the asymptotic properties of the Bernstein estimator for unbounded copula density functions. We show that the estimator converges to infinity at the corner and we establish its relative convergence when the copula density is unbounded. Also, we provide the uniform strong consistency of the estimator on every compact in the interior region. We investigate the finite sample performance of the estimator via an extensive simulation study and we compare the Bernstein copula density estimator with other nonparametric methods. Finally, we consider an empirical application where the asymmetric dependence between international equity markets (US, Canada, UK, and France) is examined.
© 2013 by Walter de Gruyter Berlin Boston
Articles in the same Issue
- Masthead
- Masthead
- Editorial
- Editorial to the special issue on Copulae of Statistics & Risk Modeling
- What makes dependence modeling challenging? Pitfalls and ways to circumvent them
- Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50
- Bernstein estimator for unbounded copula densities
- Dynamic structured copula models
Articles in the same Issue
- Masthead
- Masthead
- Editorial
- Editorial to the special issue on Copulae of Statistics & Risk Modeling
- What makes dependence modeling challenging? Pitfalls and ways to circumvent them
- Risk management with high-dimensional vine copulas: An analysis of the Euro Stoxx 50
- Bernstein estimator for unbounded copula densities
- Dynamic structured copula models
