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The class of copulas arising from squared distributions: Properties and inference

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  • Quessy, Jean-François
  • Durocher, Martin

Abstract

A very general class of multivariate copulas is introduced. These copulas arise as the dependence structures that can be extracted from random vectors whose components are squared. The main theoretical properties of the new models are investigated and general formulas for the Kendall, Spearman and tail dependence measures are derived. The construction gives birth to new dependence models, including radially asymmetric versions of popular bivariate copulas like the Plackett, Frank and Normal dependence structures, as well as to the multivariate copulas of normal variance mixture models; the latter models are suitable in arbitrary dimensions and thus are attractive for multivariate, possibly high-dimensional, asymmetric dependence modeling. Suitably adapted parameter estimation strategies are also proposed and their properties are investigated with simulations. The newly introduced models and inferential tools are illustrated on the Nutrient dataset.

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  • 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.
    • Handle: RePEc:eee:ecosta:v:12:y:2019:i:c:p:148-166
    DOI: 10.1016/j.ecosta.2019.02.002
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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. 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.
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    6. Aas, Kjersti & Czado, Claudia & Frigessi, Arnoldo & Bakken, Henrik, 2009. "Pair-copula constructions of multiple dependence," Insurance: Mathematics and Economics, Elsevier, vol. 44(2), pages 182-198, April.
    7. Anne‐Catherine Favre & Jean‐François Quessy & Marie‐Hélène Toupin, 2018. "The new family of Fisher copulas to model upper tail dependence and radial asymmetry: Properties and application to high‐dimensional rainfall data," Environmetrics, John Wiley & Sons, Ltd., vol. 29(3), May.
    8. Nelsen, Roger B. & Quesada-Molina, José Juan & Rodríguez-Lallena, José Antonio & Úbeda-Flores, Manuel, 2003. "Kendall distribution functions," Statistics & Probability Letters, Elsevier, vol. 65(3), pages 263-268, November.
    9. Kozubowski, Tomasz J. & Podgórski, Krzysztof & Rychlik, Igor, 2013. "Multivariate generalized Laplace distribution and related random fields," Journal of Multivariate Analysis, Elsevier, vol. 113(C), pages 59-72.
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    Cited by:

    1. Marius Hofert & Johanna F. Ziegel, 2021. "Matrix-Tilted Archimedean Copulas," Risks, MDPI, vol. 9(4), pages 1-24, April.
    2. Tarik Bahraoui & Jean‐François Quessy, 2022. "Tests of multivariate copula exchangeability based on Lévy measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(3), pages 1215-1243, September.
    3. Savinov, Evgeniy & Shamraeva, Victoria, 2023. "On a Rosenblatt-type transformation of multivariate copulas," Econometrics and Statistics, Elsevier, vol. 25(C), pages 39-48.
    4. Nasri, Bouchra R., 2020. "On non-central squared copulas," Statistics & Probability Letters, Elsevier, vol. 161(C).
    5. Jean-François Quessy, 2021. "On nonparametric tests of multivariate meta-ellipticity," Statistical Papers, Springer, vol. 62(5), pages 2283-2310, October.
    6. Billio Monica & Frattarolo Lorenzo & Guégan Dominique, 2021. "Multivariate radial symmetry of copula functions: finite sample comparison in the i.i.d case," Dependence Modeling, De Gruyter, vol. 9(1), pages 43-61, January.
    7. Cong, Lin & Yao, Weixin, 2021. "A Likelihood Ratio Test of a Homoscedastic Multivariate Normal Mixture Against a Heteroscedastic Multivariate Normal Mixture," Econometrics and Statistics, Elsevier, vol. 18(C), pages 79-88.

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