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Maximal non-exchangeability in dimension d

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  • Harder, Michael
  • Stadtmüller, Ulrich

Abstract

We give the maximal distance between a copula and itself when the argument is permuted for arbitrary dimension, generalizing a result for dimension two by Nelsen (2007), Klement and Mesiar (2006). Furthermore, we establish a subset of [0,1]d in which this bound might be attained. For each point in this subset we present a copula and a permutation, for which the distance in this point is maximal. In the process, we see that this subset depends on the dimension being even or odd.

Suggested Citation

  • Harder, Michael & Stadtmüller, Ulrich, 2014. "Maximal non-exchangeability in dimension d," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 31-41.
    • Handle: RePEc:eee:jmvana:v:124:y:2014:i:c:p:31-41
    DOI: 10.1016/j.jmva.2013.10.003
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    References listed on IDEAS

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    1. Fabrizio Durante & Erich Klement & Carlo Sempi & Manuel Úbeda-Flores, 2010. "Measures of non-exchangeability for bivariate random vectors," Statistical Papers, Springer, vol. 51(3), pages 687-699, September.
    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. Piotr Mikusiński & Michael Taylor, 2010. "Some approximations of n-copulas," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 72(3), pages 385-414, November.
    4. Roger Nelsen, 2007. "Extremes of nonexchangeability," Statistical Papers, Springer, vol. 48(4), pages 695-695, October.
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    Cited by:

    1. Monica Billio & Lorenzo Frattarolo & Dominique Guegan, 2017. "Multivariate Reflection Symmetry of Copula Functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01592147, HAL.
    2. Hua, Lei & Polansky, Alan & Pramanik, Paramahansa, 2019. "Assessing bivariate tail non-exchangeable dependence," Statistics & Probability Letters, Elsevier, vol. 155(C), pages 1-1.
    3. Kamnitui Noppadon & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2018. "Maximum asymmetry of copulas revisited," Dependence Modeling, De Gruyter, vol. 6(1), pages 47-62, February.

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    Keywords

    Copula; Symmetry; Shuffle of min;
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