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Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta

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  • Damjana Kokol Bukovv{s}ek
  • Tomav{z} Kov{s}ir
  • Blav{z} Mojv{s}kerc
  • Matjav{z} Omladiv{c}

Abstract

Copulas are becoming an essential tool in analyzing data thus encouraging interest in related questions. In the early stage of exploratory data analysis, say, it is helpful to know local copula bounds with a fixed value of a given measure of association. These bounds have been computed for Spearman's rho, Kendall's tau, and Blomqvist's beta. The importance of another two measures of association, Spearman's footrule and Gini's gamma, has been reconfirmed recently. It is the main purpose of this paper to fill in the gap and present the mentioned local bounds for these two measures as well. It turns out that this is a quite non-trivial endeavor as the bounds are quasi-copulas that are not copulas for certain values of the two measures. We also give relations between these two measures of association and Blomqvist's beta.

Suggested Citation

  • Damjana Kokol Bukovv{s}ek & Tomav{z} Kov{s}ir & Blav{z} Mojv{s}kerc & Matjav{z} Omladiv{c}, 2020. "Spearman's footrule and Gini's gamma: Local bounds for bivariate copulas and the exact region with respect to Blomqvist's beta," Papers 2009.06221, arXiv.org, revised Jan 2021.
    • Handle: RePEc:arx:papers:2009.06221
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    References listed on IDEAS

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    1. Marco Scarsini, 1984. "On measures of concordance," Post-Print hal-00542380, HAL.
    2. Taylor M. D., 2016. "Multivariate measures of concordance for copulas and their marginals," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, October.
    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.
    4. 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.
    5. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2001. "Distribution functions of copulas: a class of bivariate probability integral transforms," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 277-282, October.
    6. Roger Nelsen, 2007. "Extremes of nonexchangeability," Statistical Papers, Springer, vol. 48(4), pages 695-695, October.
    7. Manuela Schreyer & Roland Paulin & Wolfgang Trutschnig, 2017. "On the exact region determined by Kendall's τ and Spearman's ρ," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 79(2), pages 613-633, March.
    8. 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.
    9. Marco Scarsini, 1984. "Strong measures of concordance and convergence in probability," Post-Print hal-00542387, HAL.
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