IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v100y2009i1p243-256.html
   My bibliography  Save this article

Orthant tail dependence of multivariate extreme value distributions

Author

Listed:
  • Li, Haijun

Abstract

The orthant tail dependence describes the relative deviation of upper- (or lower-) orthant tail probabilities of a random vector from similar orthant tail probabilities of a subset of its components, and can be used in the study of dependence among extreme values. Using the conditional approach, this paper examines the extremal dependence properties of multivariate extreme value distributions and their scale mixtures, and derives the explicit expressions of orthant tail dependence parameters for these distributions. Properties of the tail dependence parameters, including their relations with other extremal dependence measures used in the literature, are discussed. Various examples involving multivariate exponential, multivariate logistic distributions and copulas of Archimedean type are presented to illustrate the results.

Suggested Citation

  • Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    • Handle: RePEc:eee:jmvana:v:100:y:2009:i:1:p:243-256
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(08)00116-4
    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. Schmid, Friedrich & Schmidt, Rafael, 2007. "Multivariate conditional versions of Spearman's rho and related measures of tail dependence," Journal of Multivariate Analysis, Elsevier, vol. 98(6), pages 1123-1140, July.
    2. Janet E. Heffernan & Jonathan A. Tawn, 2004. "A conditional approach for multivariate extreme values (with discussion)," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(3), pages 497-546, August.
    3. Genest, Christian & Rivest, Louis-Paul, 1989. "A characterization of gumbel's family of extreme value distributions," Statistics & Probability Letters, Elsevier, vol. 8(3), pages 207-211, August.
    4. Martins, A.P. & Ferreira, H., 2005. "Measuring the extremal dependence," Statistics & Probability Letters, Elsevier, vol. 73(2), pages 99-103, June.
    5. Rafael Schmidt, 2002. "Tail dependence for elliptically contoured distributions," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 55(2), pages 301-327, May.
    6. Joe, Harry & Hu, Taizhong, 1996. "Multivariate Distributions from Mixtures of Max-Infinitely Divisible Distributions," Journal of Multivariate Analysis, Elsevier, vol. 57(2), pages 240-265, May.
    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. Hua, Lei & Joe, Harry, 2012. "Tail comonotonicity: Properties, constructions, and asymptotic additivity of risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 51(2), pages 492-503.
    2. Charpentier, A. & Fougères, A.-L. & Genest, C. & Nešlehová, J.G., 2014. "Multivariate Archimax copulas," Journal of Multivariate Analysis, Elsevier, vol. 126(C), pages 118-136.
    3. Joe, Harry & Li, Haijun & Nikoloulopoulos, Aristidis K., 2010. "Tail dependence functions and vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 252-270, January.
    4. 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.
    5. Ferreira, H., 2011. "Dependence between two multivariate extremes," Statistics & Probability Letters, Elsevier, vol. 81(5), pages 586-591, May.
    6. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    7. 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.
    8. Gaißer, Sandra & Schmid, Friedrich, 2010. "On testing equality of pairwise rank correlations in a multivariate random vector," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2598-2615, November.
    9. Fabrizio Cipollini & Robert F. Engle & Giampiero M. Gallo, 2016. "Copula--based Specification of vector MEMs," Papers 1604.01338, arXiv.org.
    10. Refk Selmi & Christos Kollias & Stephanos Papadamou & Rangan Gupta, 2017. "A Copula-Based Quantile-on-Quantile Regression Approach to Modeling Dependence Structure between Stock and Bond Returns: Evidence from Historical Data of India, South Africa, UK and US," Working Papers 201747, University of Pretoria, Department of Economics.
    11. Zhang, Dalu, 2014. "Vine copulas and applications to the European Union sovereign debt analysis," International Review of Financial Analysis, Elsevier, vol. 36(C), pages 46-56.
    12. repec:hum:wpaper:sfb649dp2009-014 is not listed on IDEAS
    13. Anne‐Laure Fougères & John P. Nolan & Holger Rootzén, 2009. "Models for Dependent Extremes Using Stable Mixtures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(1), pages 42-59, March.
    14. César Garcia-Gomez & Ana Pérez & Mercedes Prieto-Alaiz, 2022. "The evolution of poverty in the EU-28: a further look based on multivariate tail dependence," Working Papers 605, ECINEQ, Society for the Study of Economic Inequality.
    15. Bücher Axel, 2014. "A note on nonparametric estimation of bivariate tail dependence," Statistics & Risk Modeling, De Gruyter, vol. 31(2), pages 151-162, June.
    16. Aristidis Nikoloulopoulos & Dimitris Karlis, 2010. "Regression in a copula model for bivariate count data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 37(9), pages 1555-1568.
    17. Alexandra Ramos & Anthony Ledford, 2009. "A new class of models for bivariate joint tails," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 219-241, January.
    18. Nadarajah, Saralees, 2015. "Expansions for bivariate copulas," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 77-84.
    19. Koen Decancq, 2014. "Copula-based measurement of dependence between dimensions of well-being," Oxford Economic Papers, Oxford University Press, vol. 66(3), pages 681-701.
    20. Lee Fawcett & David Walshaw, 2014. "Estimating the probability of simultaneous rainfall extremes within a region: a spatial approach," Journal of Applied Statistics, Taylor & Francis Journals, vol. 41(5), pages 959-976, May.
    21. Kexin Li & Jianxu Liu & Yuting Xue & Sanzidur Rahman & Songsak Sriboonchitta, 2022. "Consequences of Ignoring Dependent Error Components and Heterogeneity in a Stochastic Frontier Model: An Application to Rice Producers in Northern Thailand," Agriculture, MDPI, vol. 12(8), pages 1-17, July.

    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:100:y:2009:i:1:p:243-256. 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.