IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i1p200-222.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(09)00131-6
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Akakpo, Nathalie, 2017. "Multivariate intensity estimation via hyperbolic wavelet selection," Journal of Multivariate Analysis, Elsevier, vol. 161(C), pages 32-57.
    5. 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, pages 1-36, October.
    6. 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.
    7. 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.
    8. 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.
    9. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    10. 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.
    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Antonio Cosma & Olivier Scaillet & Rainer von Sachs, 2005. "Multiariate Wavelet-based sahpe preserving estimation for dependant observation," FAME Research Paper Series rp144, International Center for Financial Asset Management and Engineering.
    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. Kato, Takeshi, 1999. "Density estimation by truncated wavelet expansion," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 159-168, June.
    4. Gérard, Kerkyacharian & Dominique, Picard, 1997. "Limit of the quadratic risk in density estimation using linear methods," Statistics & Probability Letters, Elsevier, vol. 31(4), pages 299-312, February.
    5. Marianna Pensky, 2002. "Locally Adaptive Wavelet Empirical Bayes Estimation of a Location Parameter," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 54(1), pages 83-99, March.
    6. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    7. Faugeras, Olivier P., 2009. "A quantile-copula approach to conditional density estimation," Journal of Multivariate Analysis, Elsevier, vol. 100(9), pages 2083-2099, October.
    8. Koo, Ja-Yong & Kim, Woo-Chul, 1996. "Wavelet density estimation by approximation of log-densities," Statistics & Probability Letters, Elsevier, vol. 26(3), pages 271-278, February.
    9. 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.
    10. Jean-David Fermanian, 2012. "An overview of the goodness-of-fit test problem for copulas," Papers 1211.4416, arXiv.org.
    11. Alexandre Belloni & Victor Chernozhukov & Christian Hansen, 2011. "Inference on Treatment Effects After Selection Amongst High-Dimensional Controls," Papers 1201.0224, arXiv.org, revised May 2012.
    12. Karun Adusumilli & Taisuke Otsu, 2015. "Nonparametric instrumental regression with errors in variables," STICERD - Econometrics Paper Series /2015/585, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    13. Leblanc, Frédérique, 1996. "Wavelet linear density estimator for a discrete-time stochastic process: Lp-losses," Statistics & Probability Letters, Elsevier, vol. 27(1), pages 71-84, March.
    14. repec:hal:wpaper:hal-00834000 is not listed on IDEAS
    15. Pedro Alberto Morettin & Clélia Maria de Castro Toloi & Chang Chiann & José Carlos Simon de Miranda, 2010. "Wavelet Smoothed Empirical Copula Estimators," Brazilian Review of Finance, Brazilian Society of Finance, vol. 8(3), pages 263-281.
    16. A. Antoniadis, 1997. "Wavelets in statistics: A review," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 6(2), pages 97-130, August.
    17. Masry, Elias, 1997. "Multivariate probability density estimation by wavelet methods: Strong consistency and rates for stationary time series," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 177-193, May.
    18. Durastanti, Claudio, 2016. "Adaptive global thresholding on the sphere," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 110-132.
    19. Naono Ken, 1995. "Comparative Computations of Non-parametric Density Estimation Between Some Kernel Method and the Wavelet Method," Monte Carlo Methods and Applications, De Gruyter, vol. 1(2), pages 147-163, December.
    20. Qureshi, Saba & Rehman, Ijaz Ur & Qureshi, Fiza, 2018. "Does gold act as a safe haven against exchange rate fluctuations? The case of Pakistan rupee," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 685-708.
    21. García Treviño, E.S. & Alarcón Aquino, V. & Barria, J.A., 2019. "The radial wavelet frame density estimator," Computational Statistics & Data Analysis, Elsevier, vol. 130(C), pages 111-139.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:jmvana:v:101:y:2010:i:1:p:200-222. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.