IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v54y2013i2p255-270.html
   My bibliography  Save this article

A new rank correlation measure

Author

Listed:
  • Claudio Borroni

Abstract

A new rank correlation measure β n is proposed, so as to develop a nonparametric test of independence for two variables. β n is shown to be the symmetrized version of a measure earlier proposed by Borroni and Zenga (Stat Methods Appl 16:289–308, 2007 ). More specifically, β n is built so that it can take the opposite sign, without changing its absolute value, when the ranking of one variable is reversed. Further, the meaning of the population equivalent of β n is discussed. It is pointed out that this latter association measure vanishes not only at independence but, more generally, at indifference, that is when the two variables do not show any “tendency” to positive or negative dependence. The null distribution of β n needs an independent study: hence, the finite null variance and a table of critical values are determined. Moreover, the asymptotic null distribution of β n is derived. Finally, the performance of the test based on β n is evaluated by simulation. β n is shown to be a good competitor of some classical tests for the same problem. Copyright Springer-Verlag 2013

Suggested Citation

  • Claudio Borroni, 2013. "A new rank correlation measure," Statistical Papers, Springer, vol. 54(2), pages 255-270, May.
    • Handle: RePEc:spr:stpapr:v:54:y:2013:i:2:p:255-270
    DOI: 10.1007/s00362-011-0423-0
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00362-011-0423-0
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00362-011-0423-0?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. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    2. Javad Behboodian & Ali Dolati & Manuel Úbeda-Flores, 2007. "A multivariate version of Gini's rank association coefficient," Statistical Papers, Springer, vol. 48(2), pages 295-304, April.
    3. Claudio Borroni & Michele Zenga, 2007. "A test of concordance based on Gini’s mean difference," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 16(3), pages 289-308, 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. Claudio G. Borroni & D. Michele Cifarelli, 2017. "The influence function of Gini’s gamma," METRON, Springer;Sapienza Università di Roma, vol. 75(1), pages 17-29, April.
    2. Claudio G. Borroni, 2019. "Mutual association measures," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(4), pages 571-591, December.

    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. Ying Zhang & Chuancun Yin, 2014. "A new multivariate dependence measure based on comonotonicity," Papers 1410.7845, arXiv.org.
    2. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    3. Edoardo Berton & Lorenzo Mercuri, 2021. "An Efficient Unified Approach for Spread Option Pricing in a Copula Market Model," Papers 2112.11968, arXiv.org, revised Feb 2023.
    4. 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.
    5. Jiří Dvořák & Tomáš Mrkvička, 2022. "Graphical tests of independence for general distributions," Computational Statistics, Springer, vol. 37(2), pages 671-699, April.
    6. Liebscher Eckhard, 2017. "Copula-Based Dependence Measures For Piecewise Monotonicity," Dependence Modeling, De Gruyter, vol. 5(1), pages 198-220, August.
    7. N. Nair & P. Sankaran & B. Vineshkumar, 2012. "Characterization of distributions by properties of truncated Gini index and mean difference," METRON, Springer;Sapienza Università di Roma, vol. 70(2), pages 173-191, August.
    8. Ferreira Helena & Ferreira Marta, 2020. "Multivariate medial correlation with applications," Dependence Modeling, De Gruyter, vol. 8(1), pages 361-372, January.
    9. Salim Bouzebda, 2023. "On Weak Convergence of the Bootstrap Copula Empirical Process with Random Resample Size," Stats, MDPI, vol. 6(1), pages 1-16, February.
    10. Okimoto, Tatsuyoshi, 2014. "Asymmetric increasing trends in dependence in international equity markets," Journal of Banking & Finance, Elsevier, vol. 46(C), pages 219-232.
    11. Vanderford Courtney & Sang Yongli & Dang Xin, 2020. "Two symmetric and computationally efficient Gini correlations," Dependence Modeling, De Gruyter, vol. 8(1), pages 373-395, January.
    12. Genest, Christian & Kochar, Subhash C. & Xu, Maochao, 2009. "On the range of heterogeneous samples," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1587-1592, September.
    13. Gilbert Laffond & Jean Lainé & M. Remzi Sanver, 2020. "Metrizable preferences over preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 177-191, June.
    14. Friedrich Schmid & Rafael Schmidt, 2007. "Nonparametric inference on multivariate versions of Blomqvist’s beta and related measures of tail dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 66(3), pages 323-354, November.
    15. Marta Cardin & Elisa Pagani, 2008. "Some proposals about multivariate risk measurement," Working Papers 165, Department of Applied Mathematics, Università Ca' Foscari Venezia.
    16. Machová Renáta & Korcsmáros Enikő & Marča Roland & Esseová Monika, 2022. "An International Analysis of Consumers’ Consciousness During the Covid-19 Pandemic in Slovakia and Hungary," Folia Oeconomica Stetinensia, Sciendo, vol. 22(1), pages 130-151, June.
    17. Dolati, Ali & Genest, Christian & Kochar, Subhash C., 2008. "On the dependence between the extreme order statistics in the proportional hazards model," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 777-786, May.
    18. 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).
    19. Fuchs Sebastian, 2016. "A Biconvex Form for Copulas," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, February.
    20. 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.

    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:stpapr:v:54:y:2013:i:2:p:255-270. 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.