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Coskewness under dependence uncertainty

Author

Listed:
  • Bernard, Carole
  • Chen, Jinghui
  • Rüschendorf, Ludger
  • Vanduffel, Steven

Abstract

We study the impact of dependence uncertainty on E(X1X2⋯Xd), Xi∼Fi. Under some conditions on the Fi, explicit sharp bounds are obtained. A numerical method is provided to approximate them for arbitrary Fi. We introduce a notion of “standardized rank coskewness”, which is invariant under strictly increasing transformations and takes values in [−1,1].

Suggested Citation

  • Bernard, Carole & Chen, Jinghui & Rüschendorf, Ludger & Vanduffel, Steven, 2023. "Coskewness under dependence uncertainty," Statistics & Probability Letters, Elsevier, vol. 199(C).
    • Handle: RePEc:eee:stapro:v:199:y:2023:i:c:s0167715223000779
    DOI: 10.1016/j.spl.2023.109853
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    References listed on IDEAS

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    1. Bignozzi, Valeria & Puccetti, Giovanni, 2015. "Studying mixability with supermodular aggregating functions," Statistics & Probability Letters, Elsevier, vol. 100(C), pages 48-55.
    2. Wang, Bin & Wang, Ruodu, 2015. "Extreme negative dependence and risk aggregation," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 12-25.
    3. Roger Nelsen & Manuel Úbeda-Flores, 2012. "Directional dependence in multivariate distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(3), pages 677-685, June.
    4. Wang, Bin & Wang, Ruodu, 2011. "The complete mixability and convex minimization problems with monotone marginal densities," Journal of Multivariate Analysis, Elsevier, vol. 102(10), pages 1344-1360, November.
    5. Rüschendorf, Ludger & Uckelmann, Ludger, 2002. "On the n-Coupling Problem," Journal of Multivariate Analysis, Elsevier, vol. 81(2), pages 242-258, May.
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