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On the approximation of copulas via shuffles of Min

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  • Durante, Fabrizio
  • Sánchez, Juan Fernández

Abstract

We study a multivariate extension of shuffles of Min that has a probabilistic interpretation in terms of mutually completely dependent process. The closure properties of the class of such copulas under different types of convergence is investigated.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:10:p:1761-1767
    DOI: 10.1016/j.spl.2012.06.008
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    References listed on IDEAS

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    1. Karl Siburg & Pavel Stoimenov, 2010. "A measure of mutual complete dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 239-251, March.
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    3. Zephyr, 2010. "The city," City, Taylor & Francis Journals, vol. 14(1-2), pages 154-155, February.
    4. Puccetti, Giovanni & Scarsini, Marco, 2010. "Multivariate comonotonicity," Journal of Multivariate Analysis, Elsevier, vol. 101(1), pages 291-304, January.
    5. Baker, Rose, 2008. "An order-statistics-based method for constructing multivariate distributions with fixed marginals," Journal of Multivariate Analysis, Elsevier, vol. 99(10), pages 2312-2327, November.
    6. Dhaene, J. & Denuit, M. & Goovaerts, M. J. & Kaas, R. & Vyncke, D., 2002. "The concept of comonotonicity in actuarial science and finance: theory," Insurance: Mathematics and Economics, Elsevier, vol. 31(1), pages 3-33, August.
    7. Durante, Fabrizio & Fernández-Sánchez, Juan, 2010. "Multivariate shuffles and approximation of copulas," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1827-1834, December.
    8. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
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    Cited by:

    1. Ansari Jonathan & Rüschendorf Ludger, 2018. "Ordering risk bounds in factor models," Dependence Modeling, De Gruyter, vol. 6(1), pages 259-287, November.
    2. Carole Bernard & Oleg Bondarenko & Steven Vanduffel, 2018. "Rearrangement algorithm and maximum entropy," Annals of Operations Research, Springer, vol. 261(1), pages 107-134, February.
    3. 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.
    4. 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.
    5. Durante, Fabrizio & Fernández Sánchez, Juan & Trutschnig, Wolfgang, 2014. "Multivariate copulas with hairpin support," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 323-334.

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