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Diversity of Bivariate Concordance Measures

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  • Martynas Manstavičius

    (Faculty of Mathematics and Informatics, Institute of Mathematics, Vilnius University, Naugarduko Str. 24, LT-03225 Vilnius, Lithuania)

Abstract

We revisit the axioms of Scarsini, defining bivariate concordance measures for a pair of continuous random variables ( X , Y ) ; such measures can be understood as functions of the bivariate copula C associated with ( X , Y ) . Two constructions, investigated in the works of Edwards, Mikusiński, Taylor, and Fuchs, are generalized, yielding, in particular, examples of higher than degree-two polynomial-type concordance measures, along with examples of non-polynomial-type concordance measures, and providing an incentive to investigate possible further characterizations of such concordance measures, as was achieved by Edwards and Taylor for the degree-one case.

Suggested Citation

  • Martynas Manstavičius, 2022. "Diversity of Bivariate Concordance Measures," Mathematics, MDPI, vol. 10(7), pages 1-18, March.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:7:p:1103-:d:782285
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    References listed on IDEAS

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    1. Denuit, Michel & Mesfioui, Mhamed & Trufin, Julien, 2019. "Concordance-based predictive measures in regression models for discrete responses," LIDAM Reprints ISBA 2019047, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. 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.
    3. 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.
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    5. 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).
    6. H. H. Edwards & P. Mikusiński & M. D. Taylor, 2004. "Measures of concordance determined by D 4 -invariant copulas," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2004, pages 1-9, January.
    7. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
    8. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    9. Taylor M. D., 2016. "Multivariate measures of concordance for copulas and their marginals," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, October.
    10. 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.
    11. 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.
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