IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v64y1998i1p25-47.html
   My bibliography  Save this article

Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function

Author

Listed:
  • Drees, Holger
  • Huang, Xin

Abstract

It is well known that a bivariate distribution belongs to the domain of attraction of an extreme value distribution G if and only if the marginals belong to the domain of attraction of the univariate marginal extreme value distributions and the dependence function converges to the stable tail dependence function of G. Hall and Welsh (1984,Ann. Statist.12, 1079-1084) and Drees (1997b,Ann. Statist., to appear) addressed the problem of finding optimal rates of convergence for estimators of the extreme value index of an univariate distribution. The present paper deals with the corresponding problem for the stable tail dependence function. First an upper bound on the rate of convergence for estimators of the stable tail dependence function is established. Then it is shown that this bound is sharp by proving that it is attained by the tail empirical dependence function. Finally, we determine the limit distribution of this estimator if the dependence function satisfies a certain second-order condition.

Suggested Citation

  • Drees, Holger & Huang, Xin, 1998. "Best Attainable Rates of Convergence for Estimators of the Stable Tail Dependence Function," Journal of Multivariate Analysis, Elsevier, vol. 64(1), pages 25-47, January.
  • Handle: RePEc:eee:jmvana:v:64:y:1998:i:1:p:25-47
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(97)91708-5
    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. Einmahl, J. H. J. & Dehaan, L. & Huang, X., 1993. "Estimating a Multidimensional Extreme-Value Distribution," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 35-47, October.
    2. Stuart G. Coles & Jonathan A. Tawn, 1994. "Statistical Methods for Multivariate Extremes: An Application to Structural Design," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 43(1), pages 1-31, March.
    3. Einmahl, J. H.J. & Dekkers, A. L.M. & de Haan, L., 1989. "A moment estimator for the index of an extreme-value distribution," Other publications TiSEM 81970cb3-5b7a-4cad-9bf6-2, Tilburg University, School of Economics and Management.
    Full references (including those not matched with items on IDEAS)

    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. 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. 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.
    3. Bücher Axel, 2014. "A note on nonparametric estimation of bivariate tail dependence," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 151-162, June.
    4. de Valk, Cees, 2016. "A large deviations approach to the statistics of extreme events," Other publications TiSEM 117b3ba0-0e40-4277-b25e-d, Tilburg University, School of Economics and Management.
    5. Fátima Brilhante, M. & Ivette Gomes, M. & Pestana, Dinis, 2013. "A simple generalisation of the Hill estimator," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 518-535.
    6. Igor Fedotenkov, 2020. "A Review of More than One Hundred Pareto-Tail Index Estimators," Statistica, Department of Statistics, University of Bologna, vol. 80(3), pages 245-299.
    7. Marco Rocco, 2011. "Extreme value theory for finance: a survey," Questioni di Economia e Finanza (Occasional Papers) 99, Bank of Italy, Economic Research and International Relations Area.
    8. Phornchanok Cumperayot & Casper G. de Vries, 2006. "Large Swings in Currencies driven by Fundamentals," Tinbergen Institute Discussion Papers 06-086/2, Tinbergen Institute.
    9. Virta, Joni & Lietzén, Niko & Viitasaari, Lauri & Ilmonen, Pauliina, 2024. "Latent model extreme value index estimation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    10. Einmahl, J.H.J. & de Haan, L.F.M. & Krajina, A., 2009. "Estimating Extreme Bivariate Quantile Regions," Other publications TiSEM 007ce0a9-dd94-4301-ad62-1, Tilburg University, School of Economics and Management.
    11. Estate Khmaladze & Wolfgang Weil, 2008. "Local empirical processes near boundaries of convex bodies," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 60(4), pages 813-842, December.
    12. D. J. Rasmussen & Scott Kulp & Robert E. Kopp & Michael Oppenheimer & Benjamin H. Strauss, 2022. "Popular extreme sea level metrics can better communicate impacts," Climatic Change, Springer, vol. 170(3), pages 1-17, February.
    13. Xue-Zhong He & Youwei Li, 2017. "The adaptiveness in stock markets: testing the stylized facts in the DAX 30," Journal of Evolutionary Economics, Springer, vol. 27(5), pages 1071-1094, November.
    14. Einmahl, J.H.J. & Li, Jun & Liu, Regina, 2015. "Bridging Centrality and Extremity : Refining Empirical Data Depth using Extreme Value Statistics," Discussion Paper 2015-020, Tilburg University, Center for Economic Research.
    15. Marta Ferreira, 2024. "Extremal index: estimation and resampling," Computational Statistics, Springer, vol. 39(5), pages 2703-2720, July.
    16. Ghosh, Souvik & Resnick, Sidney, 2010. "A discussion on mean excess plots," Stochastic Processes and their Applications, Elsevier, vol. 120(8), pages 1492-1517, August.
    17. Wager, Stefan, 2014. "Subsampling extremes: From block maxima to smooth tail estimation," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 335-353.
    18. Bouye, Eric & Durlleman, Valdo & Nikeghbali, Ashkan & Riboulet, Gaël & Roncalli, Thierry, 2000. "Copulas for finance," MPRA Paper 37359, University Library of Munich, Germany.
    19. de Haan, Laurens & Canto e Castro, Luisa, 2006. "A class of distribution functions with less bias in extreme value estimation," Statistics & Probability Letters, Elsevier, vol. 76(15), pages 1617-1624, September.
    20. Charnchai Leuwattanachotinan & Casper G. de Vries, 2015. "Extreme Linkages in Financial Markets: Macro Shocks and Systemic Risk," PIER Discussion Papers 2, Puey Ungphakorn Institute for Economic Research.

    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:64:y:1998:i:1:p:25-47. 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.