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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.
Acknowledgments
H. Noh's research is supported by IAP research network P6/03 of the Belgian Government (Belgian Science Policy) and the European Research Council under the European Community's Seventh Framework Programme (FP7/2007-2013)/ERC Grant agreement no. 203650. A. El Ghouch's research is supported by IAP research network P6/03 of the Belgian Government (Belgian Science Policy), and the contract “Projet d’Actions de Recherche Concertées” (ARC) 11/16-039 of the “Communauté Française de Belgique,” granted by the “Académie Universitaire Louvain.” The authors thank two anonymous referees, the associate editor, and the coeditor for their valuable suggestions that have significantly improved the article.