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Multivariate shuffles and approximation of copulas

Author

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  • Durante, Fabrizio
  • Fernández-Sánchez, Juan

Abstract

We present and study a method for constructing multivariate copulas, which includes both the shuffles of Min and the ordinal sums. Such a method has been used in order to show that suitable transformations of a given copula constitute a dense set in the class of all copulas with respect to the L[infinity] norm.

Suggested Citation

  • Durante, Fabrizio & Fernández-Sánchez, Juan, 2010. "Multivariate shuffles and approximation of copulas," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1827-1834, December.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:23-24:p:1827-1834
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    Citations

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    Cited by:

    1. Pfeifer Dietmar & Mändle Andreas & Ragulina Olena, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Dependence Modeling, De Gruyter, vol. 5(1), pages 246-255, October.
    2. Fuchs, Sebastian & Schmidt, Klaus D., 2021. "On order statistics and Kendall’s tau," Statistics & Probability Letters, Elsevier, vol. 169(C).
    3. Fuchs Sebastian & McCord Yann, 2019. "On the lower bound of Spearman’s footrule," Dependence Modeling, De Gruyter, vol. 7(1), pages 126-132, January.
    4. Jae Youn Ahn & Sebastian Fuchs, 2020. "On Minimal Copulas under the Concordance Order," Journal of Optimization Theory and Applications, Springer, vol. 184(3), pages 762-780, March.
    5. Durante, Fabrizio & Sánchez, Juan Fernández, 2012. "On the approximation of copulas via shuffles of Min," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1761-1767.
    6. Juan Fernández Sánchez & Wolfgang Trutschnig, 2015. "Conditioning-based metrics on the space of multivariate copulas and their interrelation with uniform and levelwise convergence and Iterated Function Systems," Journal of Theoretical Probability, Springer, vol. 28(4), pages 1311-1336, December.
    7. 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.
    8. Durante, Fabrizio & Fernández Sánchez, Juan & Sempi, Carlo, 2013. "Multivariate patchwork copulas: A unified approach with applications to partial comonotonicity," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 897-905.
    9. Harder, Michael & Stadtmüller, Ulrich, 2014. "Maximal non-exchangeability in dimension d," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 31-41.
    10. Dietmar Pfeifer & Andreas Mandle & Olena Ragulina, 2017. "New copulas based on general partitions-of-unity and their applications to risk management (part II)," Papers 1709.07682, arXiv.org, revised Jan 2019.
    11. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.

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