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Maximum asymmetry of copulas revisited

Author

Listed:
  • Kamnitui Noppadon

    (Department for Mathematics, University of Salzburg, Salzburg, Austria)

  • Fernández-Sánchez Juan

    (Grupo de Investigación de Análisis Matemático, Universidad de Almería, La Cañada de San Urbano, Almería, Spain)

  • Trutschnig Wolfgang

    (Department for Mathematics, University of Salzburg, Salzburg, Austria)

Abstract

Motivated by the nice characterization of copulas A for which d∞(A, At) is maximal as established independently by Nelsen [11] and Klement & Mesiar [7], we study maximum asymmetry with respect to the conditioning-based metric D1 going back to Trutschnig [12]. Despite the fact that D1(A, At) is generally not straightforward to calculate, it is possible to provide both, a characterization and a handy representation of all copulas A maximizing D1(A, At). This representation is then used to prove the existence of copulas with full support maximizing D1(A, At). A comparison of D1- and d∞-asymmetry including some surprising examples rounds off the paper.

Suggested Citation

  • Kamnitui Noppadon & Fernández-Sánchez Juan & Trutschnig Wolfgang, 2018. "Maximum asymmetry of copulas revisited," Dependence Modeling, De Gruyter, vol. 6(1), pages 47-62, February.
    • Handle: RePEc:vrs:demode:v:6:y:2018:i:1:p:47-62:n:3
    DOI: 10.1515/demo-2018-0003
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    References listed on IDEAS

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    1. Roger Nelson, 2007. "Extremes of nonexchangeability," Statistical Papers, Springer, vol. 48(2), pages 329-336, April.
    2. Juan Fernández Sánchez & Wolfgang Trutschnig, 2016. "Some members of the class of (quasi-)copulas with given diagonal from the Markov kernel perspective," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 45(5), pages 1508-1526, March.
    3. Harder, Michael & Stadtmüller, Ulrich, 2014. "Maximal non-exchangeability in dimension d," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 31-41.
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