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Estimation of a Copula when a Covariate Affects only Marginal Distributions

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  • Irène Gijbels
  • Marek Omelka
  • Noël Veraverbeke

Abstract

type="main" xml:id="sjos12154-abs-0001"> This paper is concerned with studying the dependence structure between two random variables Y 1 and Y 2 in the presence of a covariate X, which affects both marginal distributions but not the dependence structure. This is reflected in the property that the conditional copula of Y 1 and Y 2 given X, does not depend on the value of X. This latter independence often appears as a simplifying assumption in pair-copula constructions. We introduce a general estimator for the copula in this specific setting and establish its consistency. Moreover, we consider some special cases, such as parametric or nonparametric location-scale models for the effect of the covariate X on the marginals of Y 1 and Y 2 and show that in these cases, weak convergence of the estimator, at n -rate, holds. The theoretical results are illustrated by simulations and a real data example.

Suggested Citation

  • Irène Gijbels & Marek Omelka & Noël Veraverbeke, 2015. "Estimation of a Copula when a Covariate Affects only Marginal Distributions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1109-1126, December.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:1109-1126
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    File URL: http://hdl.handle.net/10.1111/sjos.12154
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    References listed on IDEAS

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    1. Hobæk Haff, Ingrid & Aas, Kjersti & Frigessi, Arnoldo, 2010. "On the simplified pair-copula construction -- Simply useful or too simplistic?," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1296-1310, May.
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    4. Noël Veraverbeke & Irène Gijbels & Marek Omelka, 2014. "Preadjusted non-parametric estimation of a conditional distribution function," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 399-438, March.
    5. Acar, Elif F. & Genest, Christian & Nešlehová, Johanna, 2012. "Beyond simplified pair-copula constructions," Journal of Multivariate Analysis, Elsevier, vol. 110(C), pages 74-90.
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    9. Noël Veraverbeke & Marek Omelka & Irène Gijbels, 2011. "Estimation of a Conditional Copula and Association Measures," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(4), pages 766-780, December.
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    Citations

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    Cited by:

    1. Alexander Mayer & Tatsushi Oka & Dominik Wied, 2026. "Local Gaussian copula inference with structural breaks: testing dependence predictability," Papers 2603.01721, arXiv.org.
    2. Gijbels, Irène & Omelka, Marek & Veraverbeke, Noël, 2021. "Omnibus test for covariate effects in conditional copula models," Journal of Multivariate Analysis, Elsevier, vol. 186(C).
    3. Nagler, Thomas & Czado, Claudia, 2016. "Evading the curse of dimensionality in nonparametric density estimation with simplified vine copulas," Journal of Multivariate Analysis, Elsevier, vol. 151(C), pages 69-89.
    4. Nina Deliu & Brunero Liseo, 2025. "A copula-based Bayesian framework for doping detection," Computational Statistics, Springer, vol. 40(4), pages 1873-1898, April.
    5. Grazian, Clara & Dalla Valle, Luciana & Liseo, Brunero, 2022. "Approximate Bayesian conditional copulas," Computational Statistics & Data Analysis, Elsevier, vol. 169(C).
    6. Portier, François & Segers, Johan, 2018. "On the weak convergence of the empirical conditional copula under a simplifying assumption," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 160-181.
    7. Côté, Marie-Pier & Genest, Christian & Omelka, Marek, 2019. "Rank-based inference tools for copula regression, with property and casualty insurance applications," Insurance: Mathematics and Economics, Elsevier, vol. 89(C), pages 1-15.
    8. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.
    9. Lopez, Olivier, 2019. "A censored copula model for micro-level claim reserving," Insurance: Mathematics and Economics, Elsevier, vol. 87(C), pages 1-14.
    10. Gijbels, Irène & Omelka, Marek & Pešta, Michal & Veraverbeke, Noël, 2017. "Score tests for covariate effects in conditional copulas," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 111-133.
    11. Marek Omelka & Šárka Hudecová & Natalie Neumeyer, 2021. "Maximum pseudo‐likelihood estimation based on estimated residuals in copula semiparametric models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(4), pages 1433-1473, December.
    12. Bianchi, Pascal & Elgui, Kevin & Portier, François, 2023. "Conditional independence testing via weighted partial copulas," Journal of Multivariate Analysis, Elsevier, vol. 193(C).
    13. Neumeyer, Natalie & Omelka, Marek & Hudecová, Šárka, 2019. "A copula approach for dependence modeling in multivariate nonparametric time series," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 139-162.
    14. Spanhel, Fabian & Kurz, Malte S., 2016. "The partial copula: Properties and associated dependence measures," Statistics & Probability Letters, Elsevier, vol. 119(C), pages 76-83.

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