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On the lower bound of Spearman’s footrule

Author

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  • Fuchs Sebastian

    (Technische Universität Dortmund)

  • McCord Yann

    (Technische Universität Dresden)

Abstract

Úbeda-Flores showed that the range of multivariate Spearman’s footrule for copulas of dimension d ≥ 2 is contained in the interval [−1/d, 1], that the upper bound is attained exclusively by the upper Fréchet-Hoeffding bound, and that the lower bound is sharp in the case where d = 2. The present paper provides characterizations of the copulas attaining the lower bound of multivariate Spearman’s footrule in terms of the copula measure but also via the copula’s diagonal section.

Suggested Citation

  • Fuchs Sebastian & McCord Yann, 2019. "On the lower bound of Spearman’s footrule," Dependence Modeling, De Gruyter, vol. 7(1), pages 126-132, January.
    • Handle: RePEc:vrs:demode:v:7:y:2019:i:1:p:126-132:n:5
    DOI: 10.1515/demo-2019-0005
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    References listed on IDEAS

    as
    1. Lee, Paul H. & Yu, Philip L.H., 2010. "Distance-based tree models for ranking data," Computational Statistics & Data Analysis, Elsevier, vol. 54(6), pages 1672-1682, June.
    2. Durante, Fabrizio & Fernández-Sánchez, Juan, 2010. "Multivariate shuffles and approximation of copulas," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1827-1834, December.
    3. Sebastian Fuchs & Yann McCord & Klaus D. Schmidt, 2018. "Characterizations of Copulas Attaining the Bounds of Multivariate Kendall’s Tau," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 424-438, August.
    4. Taylor M. D., 2016. "Multivariate measures of concordance for copulas and their marginals," Dependence Modeling, De Gruyter, vol. 4(1), pages 1-13, October.
    5. 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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