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Multivariate copulas with hairpin support

Author

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  • Durante, Fabrizio
  • Fernández Sánchez, Juan
  • Trutschnig, Wolfgang

Abstract

The notion of a two-dimensional hairpin allows for two different extensions to the general multivariate setting—that of a sub-hairpin and that of a super-hairpin. We study existence and uniqueness of ρ-dimensional copulas whose support is contained in a sub- (or super-) hairpin and extend various results about doubly stochastic measures to the general multivariate setting. In particular, we show that each copula with hairpin support is necessarily an extreme point of the convex set of all ρ-dimensional copulas. Additionally, we calculate the corresponding Markov kernels and, using a simple analytic expression for sub- (or super-) hairpin copulas, analyze the strong interrelation with copulas having a fixed diagonal section. Several examples and graphics illustrate both the chosen approach and the main results.

Suggested Citation

  • Durante, Fabrizio & Fernández Sánchez, Juan & Trutschnig, Wolfgang, 2014. "Multivariate copulas with hairpin support," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 323-334.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:323-334
    DOI: 10.1016/j.jmva.2014.06.009
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    References listed on IDEAS

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    1. Rychlik, Tomasz, 1994. "Distributions and expectations of order statistics for possibly dependent random variables," Journal of Multivariate Analysis, Elsevier, vol. 48(1), pages 31-42, January.
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    3. Mai, Jan-Frederik & Scherer, Matthias, 2009. "Lévy-frailty copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1567-1585, August.
    4. 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.
    5. 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.
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    Cited by:

    1. Kokol Bukovšek, Damjana & Košir, Tomaž & Mojškerc, Blaž & Omladič, Matjaž, 2022. "Extreme generators of shock induced copulas," Applied Mathematics and Computation, Elsevier, vol. 429(C).
    2. repec:bpj:demode:v:6:y:2018:i:1:p:139-155:n:9 is not listed on IDEAS

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