IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v12y1991i5p429-439.html
   My bibliography  Save this article

On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions

Author

Listed:
  • Deheuvels, Paul

Abstract

We establish the functional central limit theorem and law of the iterated logarithm for the Pickands estimator of the dependence function of a bivariate extreme-value distribution. Our methods are based on general results for sums of random variables taking values in Banach spaces.

Suggested Citation

  • Deheuvels, Paul, 1991. "On the limiting behavior of the Pickands estimator for bivariate extreme-value distributions," Statistics & Probability Letters, Elsevier, vol. 12(5), pages 429-439, November.
    • Handle: RePEc:eee:stapro:v:12:y:1991:i:5:p:429-439
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(91)90032-M
    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.

    Citations

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


    Cited by:

    1. Einmahl, John H.J. & de Haan, Laurens & Sinha, Ashoke Kumar, 1997. "Estimating the spectral measure of an extreme value distribution," Stochastic Processes and their Applications, Elsevier, vol. 70(2), pages 143-171, October.
    2. Cooley, Daniel & Davis, Richard A. & Naveau, Philippe, 2010. "The pairwise beta distribution: A flexible parametric multivariate model for extremes," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2103-2117, October.
    3. Gudendorf, Gordon & Segers, Johan, 2011. "Nonparametric estimation of an extreme-value copula in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 37-47, January.
    4. Fils-Villetard, A. & Guillou, A. & Segers, J., 2005. "Projection Estimates of Constrained Functional Parameters," Discussion Paper 2005-111, Tilburg University, Center for Economic Research.
    5. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    6. Dutfoy Anne & Parey Sylvie & Roche Nicolas, 2014. "Multivariate Extreme Value Theory - A Tutorial with Applications to Hydrology and Meteorology," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-19, June.
    7. Gardes, Laurent & Girard, Stéphane, 2015. "Nonparametric estimation of the conditional tail copula," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 1-16.
    8. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    9. Jiménez, Javier Rojo & Villa-Diharce, Enrique & Flores, Miguel, 2001. "Nonparametric Estimation of the Dependence Function in Bivariate Extreme Value Distributions," Journal of Multivariate Analysis, Elsevier, vol. 76(2), pages 159-191, February.
    10. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On the distribution of Pickands coordinates in bivariate EV and GP models," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 267-295, April.
    11. Zhang, Dabao & Wells, Martin T. & Peng, Liang, 2008. "Nonparametric estimation of the dependence function for a multivariate extreme value distribution," Journal of Multivariate Analysis, Elsevier, vol. 99(4), pages 577-588, April.
    12. Fils-Villetard, A. & Guillou, A. & Segers, J., 2005. "Projection Estimates of Constrained Functional Parameters," Other publications TiSEM fe25c070-c313-4369-a6a5-8, Tilburg University, School of Economics and Management.
    13. Marcon, Giulia & Padoan, Simone & Naveau, Philippe & Muliere, Pietro & Segers, Johan, 2016. "Multivariate Nonparametric Estimation of the Pickands Dependence Function using Bernstein Polynomials," LIDAM Discussion Papers ISBA 2016020, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    14. Papastathopoulos, Ioannis & Tawn, Jonathan A., 2014. "Dependence properties of multivariate max-stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 134-140.
    15. Alireza Ahmadabadi & Burcu Hudaverdi Ucer, 2017. "Bivariate nonparametric estimation of the Pickands dependence function using Bernstein copula with kernel regression approach," Computational Statistics, Springer, vol. 32(4), pages 1515-1532, December.
    16. Gudendorf, Gordon & Segers, Johan, 2011. "Nonparametric estimation of multivariate extreme-value copulas," LIDAM Discussion Papers ISBA 2011018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Segers, J.J.J., 2004. "Non-Parametric Inference for Bivariate Extreme-Value Copulas," Discussion Paper 2004-91, Tilburg University, Center for Economic Research.
    18. Capéraà, Philippe & Fougères, Anne-Laure & Genest, Christian, 2000. "Bivariate Distributions with Given Extreme Value Attractor," Journal of Multivariate Analysis, Elsevier, vol. 72(1), pages 30-49, January.
    19. Falk, Michael & Reiss, Rolf-Dieter, 2005. "On Pickands coordinates in arbitrary dimensions," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 426-453, February.
    20. Boulin, Alexis & Di Bernardino, Elena & Laloë, Thomas & Toulemonde, Gwladys, 2022. "Non-parametric estimator of a multivariate madogram for missing-data and extreme value framework," Journal of Multivariate Analysis, Elsevier, vol. 192(C).
    21. Segers, J.J.J., 2004. "Non-Parametric Inference for Bivariate Extreme-Value Copulas," Other publications TiSEM 3e837d24-e733-407c-bfaa-f, Tilburg University, School of Economics and Management.
    22. Hu, Shuang & Peng, Zuoxiang & Segers, Johan, 2022. "Modelling multivariate extreme value distributions via Markov trees," LIDAM Discussion Papers ISBA 2022021, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    23. Segers, Johan, 2012. "Nonparametric inference for max-stable dependence : Discussion of "Statistical Modelling of Spatial Extremes" by A. C. Davison, S. Padoan and M. Ribatet, to appear in Statistical Science," LIDAM Discussion Papers ISBA 2012012, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    24. Bucher, Axel & Segers, Johan, 2013. "Extreme value copula estimation based on block maxima of a multivariate stationary time series," LIDAM Discussion Papers ISBA 2013049, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).

    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:stapro:v:12:y:1991:i:5:p:429-439. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.