Title: Some comments on copula-based regression
Authors: Holger Dette - Ruhr-Universitaet Bochum (Germany)
Ria Van Hecke - Ruhr Universitaet Bochum (Germany) [presenting]
Stanislav Volgushev - University of Toronto (Canada)
Abstract: A new semiparametric estimate of a regression function with a multivariate predictor was recently proposed, which is based on a specification of the dependence structure between the predictor and the response by means of a parametric copula. We investigate 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 copulae (with the common parametric families) are used in the estimation procedure.