Misspecification in copula-based regression
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Date
2013-10-11
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Abstract
In a recent paper Noh et al. (2013) 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 paper investigates
the effect which occurs under misspecification of the parametric model. We demonstrate that even
for a one or two dimensional predictor the error caused by a \wrong" speci fication 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 more
flexible copula models such as vine copulae (with the common parametric families) are
used in the estimation procedure.
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Keywords
copulae, curse of dimensionality, pairwise copulae,, semiparametric inference, vine copulae