IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v22y2020i3d10.1007_s11009-019-09752-2.html
   My bibliography  Save this article

Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas

Author

Listed:
  • Antonio Dalessandro

    (University College London)

  • Gareth W. Peters

    (Heriot-Watt University)

Abstract

There is now an increasingly large number of proposed concordance measures available to capture, measure and quantify different notions of dependence in stochastic processes. However, evaluation of concordance measures to quantify such types of dependence for different copula models can be challenging. In this work, we propose a class of new methods that involves a highly accurate and computationally efficient procedure to evaluate concordance measures for a given copula, applicable even when sampling from the copula is not easily achieved. In addition, this then allows us to reconstruct maps of concordance measures locally in all regions of the state space for any range of copula parameters. We believe this technique will be a valuable tool for practitioners to understand better the behaviour of copula models and associated concordance measures expressed in terms of these copula models.

Suggested Citation

  • Antonio Dalessandro & Gareth W. Peters, 2020. "Efficient and Accurate Evaluation Methods for Concordance Measures via Functional Tensor Characterizations of Copulas," Methodology and Computing in Applied Probability, Springer, vol. 22(3), pages 1089-1124, September.
    • Handle: RePEc:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09752-2
    DOI: 10.1007/s11009-019-09752-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-019-09752-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-019-09752-2?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. 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.
    2. Claudia Klüppelberg & Gabriel Kuhn & Liang Peng, 2008. "Semi‐Parametric Models for the Multivariate Tail Dependence Function – the Asymptotically Dependent Case," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 35(4), pages 701-718, December.
    3. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    4. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    5. M. Taylor, 2007. "Multivariate measures of concordance," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(4), pages 789-806, December.
    6. Takemi Yanagimoto & Masashi Okamoto, 1969. "Partial orderings of permutations and monotonicity of a rank correlation statistic," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 21(1), pages 489-506, December.
    7. Li, Haijun, 2009. "Orthant tail dependence of multivariate extreme value distributions," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 243-256, January.
    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. Martynas Manstavičius, 2022. "Diversity of Bivariate Concordance Measures," Mathematics, MDPI, vol. 10(7), pages 1-18, March.

    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. 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.
    2. Li, Haijun & Wu, Peiling, 2013. "Extremal dependence of copulas: A tail density approach," Journal of Multivariate Analysis, Elsevier, vol. 114(C), pages 99-111.
    3. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    4. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    5. Gijbels, Irène & Kika, Vojtěch & Omelka, Marek, 2021. "On the specification of multivariate association measures and their behaviour with increasing dimension," Journal of Multivariate Analysis, Elsevier, vol. 182(C).
    6. Edwards, H.H. & Taylor, M.D., 2009. "Characterizations of degree one bivariate measures of concordance," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1777-1791, September.
    7. Ferreira, Helena & Ferreira, Marta, 2012. "Tail dependence between order statistics," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 176-192.
    8. Liebscher Eckhard, 2014. "Copula-based dependence measures," Dependence Modeling, De Gruyter, vol. 2(1), pages 1-16, October.
    9. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    10. Koen Decancq, 2020. "Measuring cumulative deprivation and affluence based on the diagonal dependence diagram," METRON, Springer;Sapienza Università di Roma, vol. 78(2), pages 103-117, August.
    11. Harry Joe & Haijun Li, 2011. "Tail Risk of Multivariate Regular Variation," Methodology and Computing in Applied Probability, Springer, vol. 13(4), pages 671-693, December.
    12. Dalia Valencia & Rosa E. Lillo & Juan Romo, 2019. "A Kendall correlation coefficient between functional data," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(4), pages 1083-1103, December.
    13. Roger Nelsen & Manuel Úbeda-Flores, 2012. "Directional dependence in multivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 677-685, June.
    14. V'eronique Maume-Deschamps & Didier Rulli`ere & Khalil Said, 2017. "Asymptotic multivariate expectiles," Papers 1704.07152, arXiv.org, revised Jan 2018.
    15. Liebscher, Eckhard, 2021. "Kendall regression coefficient," Computational Statistics & Data Analysis, Elsevier, vol. 157(C).
    16. Gaißer, Sandra & Ruppert, Martin & Schmid, Friedrich, 2010. "A multivariate version of Hoeffding's Phi-Square," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2571-2586, November.
    17. Kochar, Subhash & Xu, Maochao, 2008. "A new dependence ordering with applications," Journal of Multivariate Analysis, Elsevier, vol. 99(9), pages 2172-2184, October.
    18. Li, Haijun & Hua, Lei, 2015. "Higher order tail densities of copulas and hidden regular variation," Journal of Multivariate Analysis, Elsevier, vol. 138(C), pages 143-155.
    19. César García‐Gómez & Ana Pérez & Mercedes Prieto‐Alaiz, 2021. "Copula‐based analysis of multivariate dependence patterns between dimensions of poverty in Europe," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 67(1), pages 165-195, March.
    20. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.

    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:spr:metcap:v:22:y:2020:i:3:d:10.1007_s11009-019-09752-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.