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Copula-Based Regression with Mixed Covariates

Author

Listed:
  • Saeed Aldahmani

    (Department of Statistics and Business Analytics, UAE University, Al Ain P.O. Box 15551, United Arab Emirates)

  • Othmane Kortbi

    (Department of Statistics and Business Analytics, UAE University, Al Ain P.O. Box 15551, United Arab Emirates)

  • Mhamed Mesfioui

    (Département de Mathématiques et d’Informatique, Université du Québec à Trois-Rivières, Trois-Rivières, QC G9A 5H7, Canada)

Abstract

In this paper, we focused on developing copula-based modeling procedures that effectively capture the dependence between response and explanatory variables. Building upon the work of Noh et al. (J. Am. Stat. Assoc. 2013, 108, 676–688) we extended copula-based regression to accommodate both continuous and discrete covariates. Specifically, we explored the construction of copulas to estimate the conditional mean of the response variable given the covariates, elucidating the relationship between copula structures and marginal distributions. We considered various estimation methods for copulas and distribution functions, presenting a diverse array of estimators for the conditional mean function. These estimators range from non-parametric to semi-parametric and fully parametric, offering flexibility in modeling regression relationships. An adapted algorithm is applied to construct copulas and simulations are carried out to replicate datasets, estimate prediction model parameters, and compare with the OLS method. The practicality and efficacy of our proposed methodologies, grounded in the principles of copula-based regression, are substantiated through methodical simulation studies.

Suggested Citation

  • Saeed Aldahmani & Othmane Kortbi & Mhamed Mesfioui, 2024. "Copula-Based Regression with Mixed Covariates," Mathematics, MDPI, vol. 12(22), pages 1-15, November.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:22:p:3525-:d:1518809
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    References listed on IDEAS

    as
    1. Hohsuk Noh & Anouar El Ghouch & Ingrid Van Keilegom, 2015. "Semiparametric Conditional Quantile Estimation Through Copula-Based Multivariate Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(2), pages 167-178, April.
    2. Noh, Hohsuk & El Ghouch, Anouar & Van Keilegom, Ingrid, 2015. "Semiparametric Conditional Quantile Estimation Through Copula-Based Multivariate Models," LIDAM Reprints ISBA 2015013, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. M. Mesfioui & T. Bouezmarni & M. Belalia, 2023. "Copula-based link functions in binary regression models," Statistical Papers, Springer, vol. 64(2), pages 557-585, April.
    4. Nicolai Hans & Nadja Klein & Florian Faschingbauer & Michael Schneider & Andreas Mayr, 2023. "Boosting distributional copula regression," Biometrics, The International Biometric Society, vol. 79(3), pages 2298-2310, September.
    5. Noh, Hohsuk & El Ghouch, Anouar & Bouezmarni, Taoufik, 2013. "Copula-Based Regression Estimation and Inference," LIDAM Reprints ISBA 2013045, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    6. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
    7. Smith, Michael Stanley, 2023. "Implicit Copulas: An Overview," Econometrics and Statistics, Elsevier, vol. 28(C), pages 81-104.
    8. Hohsuk Noh & Anouar El Ghouch & Taoufik Bouezmarni, 2013. "Copula-Based Regression Estimation and Inference," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 676-688, June.
    9. Rémillard, Bruno & Nasri, Bouchra & Bouezmarni, Taoufik, 2017. "On copula-based conditional quantile estimators," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 14-20.
    10. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
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