A Linear Approximation to Copula Regression

Recently, Parsa and Klugman (2011) proposed a generalization of ordinary least squares regression, which they called copula regression. Though theoretically appealing, implementation, especially calibration, of copula regression is generally more involved than for generalized linear models. In this paper a linear approximation to copula regression, for which implementation is similar to that for least squares regression, will be introduced. We proceed by investigating the connection between the proposed approximation to copula regression, and copula regression itself. In particular, we develop a set of criteria which ensure a predictable bias in the estimates from the linear approximation to copula regression.