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On the family of multivariate chi-square copulas

Author

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  • Quessy, Jean-François
  • Rivest, Louis-Paul
  • Toupin, Marie-Hélène

Abstract

This paper explores the theoretical properties and the practical usefulness of the general family of chi-square copulas that recently appeared in the literature. This class of dependence structures is very attractive, as it generalizes the Gaussian copula and allows for flexible modeling for high-dimensional random vectors. On one hand, expressions for the copula and the density in the bivariate and the multivariate case are derived and many theoretical properties are investigated, including expressions for popular measures of dependence, levels of asymmetry and constraints on the Kendall’s tau matrix. On the other hand, two applications of the chi-square copulas are developed, namely parameter estimation and spatial interpolation.

Suggested Citation

  • Quessy, Jean-François & Rivest, Louis-Paul & Toupin, Marie-Hélène, 2016. "On the family of multivariate chi-square copulas," Journal of Multivariate Analysis, Elsevier, vol. 152(C), pages 40-60.
    • Handle: RePEc:eee:jmvana:v:152:y:2016:i:c:p:40-60
    DOI: 10.1016/j.jmva.2016.07.007
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    References listed on IDEAS

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    1. Christian Genest & Jean‐François Quessy & Bruno Rémillard, 2006. "Goodness‐of‐fit Procedures for Copula Models Based on the Probability Integral Transformation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(2), pages 337-366, June.
    2. Roger Nelsen, 2007. "Extremes of nonexchangeability," Statistical Papers, Springer, vol. 48(4), pages 695-695, October.
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    Cited by:

    1. Nasri, Bouchra R. & Rémillard, Bruno N. & Bouezmarni, Taoufik, 2019. "Semi-parametric copula-based models under non-stationarity," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 347-365.
    2. Jean-François Quessy, 2021. "On nonparametric tests of multivariate meta-ellipticity," Statistical Papers, Springer, vol. 62(5), pages 2283-2310, October.
    3. Marius Hofert & Johanna F. Ziegel, 2021. "Matrix-Tilted Archimedean Copulas," Risks, MDPI, vol. 9(4), pages 1-24, April.
    4. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.
    5. Nasri, Bouchra R., 2020. "On non-central squared copulas," Statistics & Probability Letters, Elsevier, vol. 161(C).
    6. Quessy, Jean-François & Durocher, Martin, 2019. "The class of copulas arising from squared distributions: Properties and inference," Econometrics and Statistics, Elsevier, vol. 12(C), pages 148-166.
    7. Bahraoui Tarik & Bouezmarni Taoufik & Quessy Jean-François, 2018. "Testing the symmetry of a dependence structure with a characteristic function," Dependence Modeling, De Gruyter, vol. 6(1), pages 331-355, December.

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