IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v123y2014icp85-95.html
   My bibliography  Save this article

Geometric interpretation of the residual dependence coefficient

Author

Listed:
  • Nolde, Natalia

Abstract

The residual dependence coefficient was originally introduced by Ledford and Tawn (1996) [25] as a measure of residual dependence between extreme values in the presence of asymptotic independence. We present a geometric interpretation of this coefficient with the additional assumptions that the random samples from a given distribution can be scaled to converge onto a limit set and that the marginal distributions have Weibull-type tails. This result leads to simple and intuitive computations of the residual dependence coefficient for a variety of distributions.

Suggested Citation

  • Nolde, Natalia, 2014. "Geometric interpretation of the residual dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 85-95.
    • Handle: RePEc:eee:jmvana:v:123:y:2014:i:c:p:85-95
    DOI: 10.1016/j.jmva.2013.08.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X13001796
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2013.08.018?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. Hashorva, Enkelejd, 2010. "On the residual dependence index of elliptical distributions," Statistics & Probability Letters, Elsevier, vol. 80(13-14), pages 1070-1078, July.
    2. Balkema, A.A. & Embrechts, P. & Nolde, N., 2010. "Meta densities and the shape of their sample clouds," Journal of Multivariate Analysis, Elsevier, vol. 101(7), pages 1738-1754, August.
    3. Anthony W. Ledford & Jonathan A. Tawn, 1997. "Modelling Dependence within Joint Tail Regions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 59(2), pages 475-499.
    4. Peng, L., 1999. "Estimation of the coefficient of tail dependence in bivariate extremes," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 399-409, July.
    5. Melanie Frick, 2012. "Measures of multivariate asymptotic dependence and their relation to spectral expansions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(6), pages 819-831, August.
    6. Cambanis, Stamatis & Huang, Steel & Simons, Gordon, 1981. "On the theory of elliptically contoured distributions," Journal of Multivariate Analysis, Elsevier, vol. 11(3), pages 368-385, September.
    7. Hua, Lei & Joe, Harry, 2011. "Tail order and intermediate tail dependence of multivariate copulas," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1454-1471, November.
    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. Lars Nørvang Andersen & Patrick J. Laub & Leonardo Rojas-Nandayapa, 2018. "Efficient Simulation for Dependent Rare Events with Applications to Extremes," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 385-409, March.
    2. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    3. Majid Asadi & Somayeh Zarezadeh, 2020. "A unified approach to constructing correlation coefficients between random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 83(6), pages 657-676, August.
    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. Hu, Shuang & Peng, Zuoxiang & Nadarajah, Saralees, 2022. "Tail dependence functions of the bivariate Hüsler–Reiss model," Statistics & Probability Letters, Elsevier, vol. 180(C).

    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. 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.
    2. Fung, Thomas & Seneta, Eugene, 2021. "Tail asymptotics for the bivariate equi-skew generalized hyperbolic distribution and its Variance-Gamma special case," Statistics & Probability Letters, Elsevier, vol. 178(C).
    3. Asimit, Alexandru V. & Gerrard, Russell, 2016. "On the worst and least possible asymptotic dependence," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 218-234.
    4. Asimit, Alexandru V. & Gerrard, Russell & Hou, Yanxi & Peng, Liang, 2016. "Tail dependence measure for examining financial extreme co-movements," Journal of Econometrics, Elsevier, vol. 194(2), pages 330-348.
    5. Michael Falk & René Michel, 2006. "Testing for Tail Independence in Extreme Value models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(2), pages 261-290, June.
    6. Goegebeur, Yuri & Guillou, Armelle & Ho, Nguyen Khanh Le & Qin, Jing, 2020. "Robust nonparametric estimation of the conditional tail dependence coefficient," Journal of Multivariate Analysis, Elsevier, vol. 178(C).
    7. Lorenzo Ricci & David Veredas, 2012. "TailCoR," Working Papers 1227, Banco de España.
      • Sla{dj}ana Babi'c & Christophe Ley & Lorenzo Ricci & David Veredas, 2020. "TailCoR," Papers 2011.14817, arXiv.org.
    8. Das, Bikramjit & Fasen-Hartmann, Vicky, 2024. "On heavy-tailed risks under Gaussian copula: The effects of marginal transformation," Journal of Multivariate Analysis, Elsevier, vol. 202(C).
    9. Fung, Thomas & Seneta, Eugene, 2016. "Tail asymptotics for the bivariate skew normal," Journal of Multivariate Analysis, Elsevier, vol. 144(C), pages 129-138.
    10. Simpson, Emma S. & Wadsworth, Jennifer L. & Tawn, Jonathan A., 2021. "A geometric investigation into the tail dependence of vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    11. Di Bernardino, Elena & Maume-Deschamps, Véronique & Prieur, Clémentine, 2013. "Estimating a bivariate tail: A copula based approach," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 81-100.
    12. Das Bikramjit & Fasen-Hartmann Vicky, 2019. "Conditional excess risk measures and multivariate regular variation," Statistics & Risk Modeling, De Gruyter, vol. 36(1-4), pages 1-23, December.
    13. Raphaël Huser & Thomas Opitz & Emeric Thibaud, 2021. "Max‐infinitely divisible models and inference for spatial extremes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(1), pages 321-348, March.
    14. Christophe Dutang & Yuri Goegebeur & Armelle Guillou, 2016. "Robust and Bias-Corrected Estimation of the Probability of Extreme Failure Sets," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 78(1), pages 52-86, February.
    15. Balakrishnan, N. & Hashorva, E., 2013. "Scale mixtures of Kotz–Dirichlet distributions," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 48-58.
    16. Lars Nørvang Andersen & Patrick J. Laub & Leonardo Rojas-Nandayapa, 2018. "Efficient Simulation for Dependent Rare Events with Applications to Extremes," Methodology and Computing in Applied Probability, Springer, vol. 20(1), pages 385-409, March.
    17. Tankov, Peter, 2016. "Tails of weakly dependent random vectors," Journal of Multivariate Analysis, Elsevier, vol. 145(C), pages 73-86.
    18. Y Hoga, 2018. "A structural break test for extremal dependence in β-mixing random vectors," Biometrika, Biometrika Trust, vol. 105(3), pages 627-643.
    19. Lei Hua, 2016. "A Note on Upper Tail Behavior of Liouville Copulas," Risks, MDPI, vol. 4(4), pages 1-10, November.
    20. Liu, Aiai & Hou, Yanxi & Peng, Liang, 2015. "Interval estimation for a measure of tail dependence," Insurance: Mathematics and Economics, Elsevier, vol. 64(C), pages 294-305.

    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:123:y:2014:i:c:p:85-95. 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.