A GLM approach to estimating copula models

Consider the problem of estimating parameter(s) of a copula which provides joint distribution for X₁, X₂, ..., X_p. This article employs concept of the generalized linear model (glm) to estimate parameter(s) of a given copula. More precisely, it considers marginal cumulative distributions Fx₂(.)Fx₃(.)...,Fx_P(.) as covariate information about Fx₁(.) Then, it estimates copulas parameter(s) by minimizing mean-squared distance between Fx₁(.) and conditional expectation E(Fx₁(.)Fx₂(.) Fx₃(.)...,Fx_P(.))Several properties of this new approach, say GLM-method, have been explored. A simulation study has been conducted to make a comparison among GLM-method, Kendals tau, Spearmans rho, the pml, and Copula-quantile regression. Based upon such simulation study, one may conjecture that for the multivariate elliptical distributions (including normal, t-student, etc.) the GLM-method provides an appropriate result, in the sense of Cramér-von Mises distance, compared to other nonparametric estimation methods.