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Some Comments on Copula-Based Regression
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DOI：10.1080/01621459.2014.916577.png)
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Abstract
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In a recent article, Noh, El Ghouch, and Bouezmarni proposed a new semiparametric estimate of a regression function with a multivariate predictor, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. This comment investigates the effect which occurs under misspecification of the parametric model. We demonstrate by means of several examples that even for a one or two-dimensional predictor the error caused by a wrong specification of the parametric family is rather severe, if the regression is not monotone in one of the components of the predictor. Moreover, we also show that these problems occur for all of the commonly used copula families and we illustrate in several examples that the copula-based regression may lead to invalid results even when flexible copula models such as vine copulas (with the common parametric families) are used in the estimation procedure.
Keywords:
Curse of dimensionality
Copulas
Pairwise copulas
Vine copulas
Semiparametric inference
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