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Thresholding methods to estimate copula density

Author

Listed:
  • Autin, F.
  • Le Pennec, E.
  • Tribouley, K.

Abstract

This paper deals with the problem of multivariate copula density estimation. Using wavelet methods we provide two shrinkage procedures based on thresholding rules for which knowledge of the regularity of the copula density to be estimated is not necessary. These methods, said to be adaptive, have proved to be very effective when adopting the minimax and the maxiset approaches. Moreover we show that these procedures can be discriminated in the maxiset sense. We provide an estimation algorithm and evaluate its properties using simulation. Finally, we propose a real life application for financial data.

Suggested Citation

  • Autin, F. & Le Pennec, E. & Tribouley, K., 2010. "Thresholding methods to estimate copula density," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 200-222, January.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:200-222
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    References listed on IDEAS

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    1. K. Tribouley, 1995. "Practical estimation of multivariate densities using wavelet methods," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 49(1), pages 41-62, March.
    2. Kerkyacharian, G. & Picard, D., 1992. "Density estimation in Besov spaces," Statistics & Probability Letters, Elsevier, vol. 13(1), pages 15-24, January.
    3. Genest, Christian & Masiello, Esterina & Tribouley, Karine, 2009. "Estimating copula densities through wavelets," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 170-181, April.
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    Cited by:

    1. Göran Kauermann & Christian Schellhase & David Ruppert, 2013. "Flexible Copula Density Estimation with Penalized Hierarchical B-splines," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(4), pages 685-705, December.
    2. Morettin Pedro A. & Toloi Clelia M.C. & Chiann Chang & de Miranda José C.S., 2011. "Wavelet Estimation of Copulas for Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-31, October.
    3. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    4. Di Bernardino Elena & Rullière Didier, 2013. "On certain transformations of Archimedean copulas: Application to the non-parametric estimation of their generators," Dependence Modeling, De Gruyter, vol. 1(2013), pages 1-36, October.
    5. Qu, Leming & Yin, Wotao, 2012. "Copula density estimation by total variation penalized likelihood with linear equality constraints," Computational Statistics & Data Analysis, Elsevier, vol. 56(2), pages 384-398.
    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. Ghislaine Gayraud & Karine Tribouley, 2011. "A goodness-of-fit test for copula densities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 20(3), pages 549-573, November.
    8. Akakpo, Nathalie, 2017. "Multivariate intensity estimation via hyperbolic wavelet selection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 32-57.
    9. Sebastian Kiwitt & Natalie Neumeyer, 2013. "A note on testing independence by a copula-based order selection approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 62-82, March.
    10. O. Chatrabgoun & G. Parham & R. Chinipardaz, 2017. "A Legendre multiwavelets approach to copula density estimation," Statistical Papers, Springer, vol. 58(3), pages 673-690, September.
    11. Pengfei Wei & Zhenzhou Lu & Jingwen Song, 2014. "Moment‐Independent Sensitivity Analysis Using Copula," Risk Analysis, John Wiley & Sons, vol. 34(2), pages 210-222, February.

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