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Copula-Based Regression Estimation and Inference

Author

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  • Hohsuk Noh
  • Anouar El Ghouch
  • Taoufik Bouezmarni

Abstract

We investigate a new approach to estimating a regression function based on copulas. The main idea behind this approach is to write the regression function in terms of a copula and marginal distributions. Once the copula and the marginal distributions are estimated, we use the plug-in method to construct our new estimator. Because various methods are available in the literature for estimating both a copula and a distribution, this idea provides a rich and flexible family of regression estimators. We provide some asymptotic results related to this copula-based regression modeling when the copula is estimated via profile likelihood and the marginals are estimated nonparametrically. We also study the finite sample performance of the estimator and illustrate its usefulness by analyzing data from air pollution studies.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:502:p:676-688
    DOI: 10.1080/01621459.2013.783842
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    Cited by:

    1. Paul R. Dewick & Shuangzhe Liu & Yonghui Liu & Tiefeng Ma, 2023. "Elliptical and Skew-Elliptical Regression Models and Their Applications to Financial Data Analytics," JRFM, MDPI, vol. 16(7), pages 1-20, June.
    2. Kraus, Daniel & Czado, Claudia, 2017. "D-vine copula based quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 110(C), pages 1-18.
    3. 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.
    4. Chang, Bo & Joe, Harry, 2019. "Prediction based on conditional distributions of vine copulas," Computational Statistics & Data Analysis, Elsevier, vol. 139(C), pages 45-63.
    5. Mohamad Khoirun Najib & Sri Nurdiati & Ardhasena Sopaheluwakan, 2022. "Multivariate fire risk models using copula regression in Kalimantan, Indonesia," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 113(2), pages 1263-1283, September.
    6. He, Yong & Zhang, Xinsheng & Zhang, Liwen, 2018. "Variable selection for high dimensional Gaussian copula regression model: An adaptive hypothesis testing procedure," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 132-150.
    7. Hamori, Shigeyuki & Motegi, Kaiji & Zhang, Zheng, 2020. "Copula-based regression models with data missing at random," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    8. Rémillard, Bruno & Nasri, Bouchra & Bouezmarni, Taoufik, 2017. "On copula-based conditional quantile estimators," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 14-20.
    9. Sifat, Imtiaz & Ghafoor, Abdul & Ah Mand, Abdollah, 2021. "The COVID-19 pandemic and speculation in energy, precious metals, and agricultural futures," Journal of Behavioral and Experimental Finance, Elsevier, vol. 30(C).
    10. 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.
    11. Xu, Qifa & Fan, Zhenhua & Jia, Weiyin & Jiang, Cuixia, 2020. "Fault detection of wind turbines via multivariate process monitoring based on vine copulas," Renewable Energy, Elsevier, vol. 161(C), pages 939-955.
    12. Maximilian Coblenz & Simon Holz & Hans‐Jörg Bauer & Oliver Grothe & Rainer Koch, 2020. "Modelling fuel injector spray characteristics in jet engines by using vine copulas," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 69(4), pages 863-886, August.
    13. Zhu, Kailun & Kurowicka, Dorota & Nane, Gabriela F., 2021. "Simplified R-vine based forward regression," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).
    14. Tepegjozova Marija & Zhou Jing & Claeskens Gerda & Czado Claudia, 2022. "Nonparametric C- and D-vine-based quantile regression," Dependence Modeling, De Gruyter, vol. 10(1), pages 1-21, January.
    15. Mojirsheibani, Majid, 2021. "On classification with nonignorable missing data," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    16. Czado, Claudia & Ivanov, Eugen & Okhrin, Yarema, 2019. "Modelling temporal dependence of realized variances with vines," Econometrics and Statistics, Elsevier, vol. 12(C), pages 198-216.

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