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Concordance measures for multivariate non-continuous random vectors

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  • Mesfioui, Mhamed
  • Quessy, Jean-François

Abstract

A notion of multivariate concordance suitable for non-continuous random variables is defined and many of its properties are established. This allows the definition of multivariate, non-continuous versions of Kendall's tau, Spearman's rho and Spearman's footrule, which are concordance measures. Since the maximum values of these association measures are not +1 in general, a special attention is given to the computation of upper bounds. The latter turn out to be multivariate generalizations of earlier findings made by Neslehová (2007) [9] and Denuit and Lambert (2005) [2]. They are easy to compute and can be estimated from a data set of (possibly) discontinuous random vectors. Corrected versions are considered as well.

Suggested Citation

  • Mesfioui, Mhamed & Quessy, Jean-François, 2010. "Concordance measures for multivariate non-continuous random vectors," Journal of Multivariate Analysis, Elsevier, vol. 101(10), pages 2398-2410, November.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:10:p:2398-2410
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    References listed on IDEAS

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    1. Joe, Harry, 1990. "Multivariate concordance," Journal of Multivariate Analysis, Elsevier, vol. 35(1), pages 12-30, October.
    2. Manuel Úbeda-Flores, 2005. "Multivariate versions of Blomqvist’s beta and Spearman’s footrule," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 57(4), pages 781-788, December.
    3. Genest, Christian & Nešlehová, Johanna, 2007. "A Primer on Copulas for Count Data," ASTIN Bulletin, Cambridge University Press, vol. 37(2), pages 475-515, November.
    4. Denuit, Michel & Lambert, Philippe, 2005. "Constraints on concordance measures in bivariate discrete data," Journal of Multivariate Analysis, Elsevier, vol. 93(1), pages 40-57, March.
    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.
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    Cited by:

    1. Genest, Christian & Nešlehová, Johanna G. & Rémillard, Bruno, 2013. "On the estimation of Spearman’s rho and related tests of independence for possibly discontinuous multivariate data," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 214-228.
    2. Pinto Da Costa, Joaquim & Roque, Luís A.C. & Soares, Carlos, 2015. "The weighted rank correlation coefficient rW2 in the case of ties," Statistics & Probability Letters, Elsevier, vol. 99(C), pages 20-26.
    3. Faugeras, Olivier P., 2015. "Maximal coupling of empirical copulas for discrete vectors," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 179-186.
    4. Denuit, Michel & Mesfoui, Mhamed & Trufin, Julien, 2019. "Concordance-based predictive measures in regression models for discrete responses," LIDAM Discussion Papers ISBA 2019005, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Denuit, Michel & Mesfioui, Mhamet & Trufin, Julien, 2016. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," LIDAM Discussion Papers ISBA 2016046, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Mhamed Mesfioui & Julien Trufin, 2022. "Bounds on Multivariate Kendall’s Tau and Spearman’s Rho for Zero-Inflated Continuous Variables and their Application to Insurance," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 1051-1059, June.
    7. Michel Denuit & Mhamed Mesfioui & Julien Trufin, 2019. "Bounds on Concordance-Based Validation Statistics in Regression Models for Binary Responses," Methodology and Computing in Applied Probability, Springer, vol. 21(2), pages 491-509, June.
    8. Martynas Manstavičius, 2022. "Diversity of Bivariate Concordance Measures," Mathematics, MDPI, vol. 10(7), pages 1-18, March.

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