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Bernstein estimator for unbounded copula densities

Author

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  • Bouezmarni, Taoufik
  • El Ghouch, Anouar
  • Taamouti, Abderrahim

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.
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Suggested Citation

  • Bouezmarni, Taoufik & El Ghouch, Anouar & Taamouti, Abderrahim, 2013. "Bernstein estimator for unbounded copula densities," LIDAM Reprints ISBA 2013047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    • Handle: RePEc:aiz:louvar:2013047
    Note: In : Statistics and Risk Modeling with Applications in Finance and Insurance, vol. 30, no.4, p. 343-360 (2013)
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    Cited by:

    1. Rémillard, Bruno & Nasri, Bouchra & Bouezmarni, Taoufik, 2017. "On copula-based conditional quantile estimators," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 14-20.
    2. Harris, A.R. & Rogers, Michelle Marinich & Miller, Carol J. & McElmurry, Shawn P. & Wang, Caisheng, 2015. "Residential emissions reductions through variable timing of electricity consumption," Applied Energy, Elsevier, vol. 158(C), pages 484-489.
    3. Ouimet, Frédéric, 2021. "Asymptotic properties of Bernstein estimators on the simplex," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    4. Shahid Latif & Slobodan P. Simonovic, 2022. "Nonparametric Approach to Copula Estimation in Compounding The Joint Impact of Storm Surge and Rainfall Events in Coastal Flood Analysis," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 36(14), pages 5599-5632, November.
    5. Eddie Anderson & Artem Prokhorov & Yajing Zhu, 2020. "A Simple Estimator of Two‐Dimensional Copulas, with Applications," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 82(6), pages 1375-1412, December.
    6. Gery Geenens & Arthur Charpentier & Davy Paindaveine, 2014. "Probit Transformation for Nonparametric Kernel Estimation of the Copula Density," Working Papers ECARES ECARES 2014-23, ULB -- Universite Libre de Bruxelles.
    7. Steven Abrams & Paul Janssen & Jan Swanepoel & Noël Veraverbeke, 2020. "Nonparametric estimation of the cross ratio function," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(3), pages 771-801, June.

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