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Multivariate copulas, quasi-copulas and lattices

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  • Fernández-Sánchez, Juan
  • Nelsen, Roger B.
  • Úbeda-Flores, Manuel

Abstract

We investigate some properties of the partially ordered sets of multivariate copulas and quasi-copulas. Whereas the set of bivariate quasi-copulas is a complete lattice, which is order-isomorphic to the Dedekind-MacNeille completion of the set of bivariate copulas, we show that this is not the case in higher dimensions.

Suggested Citation

  • Fernández-Sánchez, Juan & Nelsen, Roger B. & Úbeda-Flores, Manuel, 2011. "Multivariate copulas, quasi-copulas and lattices," Statistics & Probability Letters, Elsevier, vol. 81(9), pages 1365-1369, September.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:9:p:1365-1369
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    References listed on IDEAS

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    1. Alsina, Claudi & Nelsen, Roger B. & Schweizer, Berthold, 1993. "On the characterization of a class of binary operations on distribution functions," Statistics & Probability Letters, Elsevier, vol. 17(2), pages 85-89, May.
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    Cited by:

    1. Fabrizio Durante & Juan Fernández-Sánchez & Wolfgang Trutschnig & Manuel Úbeda-Flores, 2020. "On the Size of Subclasses of Quasi-Copulas and Their Dedekind–MacNeille Completion," Mathematics, MDPI, vol. 8(12), pages 1-11, December.
    2. Jonathan Ansari & Eva Lutkebohmert & Ariel Neufeld & Julian Sester, 2022. "Improved Robust Price Bounds for Multi-Asset Derivatives under Market-Implied Dependence Information," Papers 2204.01071, arXiv.org, revised Sep 2023.
    3. Benth Fred Espen & Nunno Giulia Di & Schroers Dennis, 2022. "A topological proof of Sklar’s theorem in arbitrary dimensions," Dependence Modeling, De Gruyter, vol. 10(1), pages 22-28, January.
    4. Nelsen, Roger B. & Úbeda-Flores, Manuel, 2012. "How close are pairwise and mutual independence?," Statistics & Probability Letters, Elsevier, vol. 82(10), pages 1823-1828.
    5. repec:bpj:demode:v:6:y:2018:i:1:p:139-155:n:9 is not listed on IDEAS

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    Keywords

    Copula Lattice Quasi-copula;

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