IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v52y2008i7p3806-3819.html
   My bibliography  Save this article

Linear B-spline copulas with applications to nonparametric estimation of copulas

Author

Listed:
  • Shen, Xiaojing
  • Zhu, Yunmin
  • Song, Lixin

Abstract

In this paper, we propose a method for constructing a new class of copulas. They are called linear B-spline copulas which are a good approximation of a given complicated copula by using finite numbers of values of this copula without the loss of some essential properties. Moreover, rigorous analysis shows that the empirical linear B-spline copulas are more effective than empirical copulas to estimate perfectly dependent copulas. For the cases of nonperfectly dependent copulas, simulations show that the empirical linear B-spline copulas also improve the empirical copulas to estimate the underlying copula structure. Furthermore, we compare the performance of parametric estimation of copulas based on the empirical copulas with that based on the empirical linear B-spline copulas by simulations. In most of the cases, the latter are better than the former.

Suggested Citation

  • Shen, Xiaojing & Zhu, Yunmin & Song, Lixin, 2008. "Linear B-spline copulas with applications to nonparametric estimation of copulas," Computational Statistics & Data Analysis, Elsevier, vol. 52(7), pages 3806-3819, March.
  • Handle: RePEc:eee:csdana:v:52:y:2008:i:7:p:3806-3819
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(08)00006-6
    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. Jean-David FERMANIAN & Olivier SCAILLET, 2003. "Nonparametric Estimation of Copulas for Time Series," FAME Research Paper Series rp57, International Center for Financial Asset Management and Engineering.
    2. Dhaene, Jan & Goovaerts, Marc J., 1996. "Dependency of Risks and Stop-Loss Order1," ASTIN Bulletin: The Journal of the International Actuarial Association, Cambridge University Press, vol. 26(2), pages 201-212, November.
    3. Kim, Gunky & Silvapulle, Mervyn J. & Silvapulle, Paramsothy, 2007. "Comparison of semiparametric and parametric methods for estimating copulas," Computational Statistics & Data Analysis, Elsevier, vol. 51(6), pages 2836-2850, March.
    4. Michel Denuit, 2004. "Nonparametric Tests for Positive Quadrant Dependence," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(3), pages 422-450.
    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. 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. Dalla Valle, Luciana & De Giuli, Maria Elena & Tarantola, Claudia & Manelli, Claudio, 2016. "Default probability estimation via pair copula constructions," European Journal of Operational Research, Elsevier, vol. 249(1), pages 298-311.
    3. Diks, Cees & Panchenko, Valentyn & van Dijk, Dick, 2010. "Out-of-sample comparison of copula specifications in multivariate density forecasts," Journal of Economic Dynamics and Control, Elsevier, vol. 34(9), pages 1596-1609, September.
    4. repec:eee:csdana:v:112:y:2017:i:c:p:99-113 is not listed on IDEAS
    5. Nadja Klein & Thomas Kneib & Giampiero Marra & Rosalba Radice & Slawa Rokicki & Mark E. McGovern, 2018. "Mixed Binary-Continuous Copula Regression Models with Application to Adverse Birth Outcomes," CHaRMS Working Papers 18-06, Centre for HeAlth Research at the Management School (CHaRMS).
    6. 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.
    7. 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.
    8. Hernández-Lobato, José Miguel & Suárez, Alberto, 2011. "Semiparametric bivariate Archimedean copulas," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2038-2058, June.
    9. Giampiero Marra & Rosalba Radice & Till Bärnighausen & Simon N. Wood & Mark E. McGovern, 2017. "A Simultaneous Equation Approach to Estimating HIV Prevalence With Nonignorable Missing Responses," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 484-496, April.

    More about this item

    Statistics

    Access and download statistics

    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:csdana:v:52:y:2008:i:7:p:3806-3819. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/csda .

    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 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.

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.