Payandeh Najafabadi, Amir T.

Qazvini, Marjan

Communications in Statistics - Simulation and Computation

Consider the problem of estimating parameter(s) of a copula which provides joint distribution for X1, X2, ..., Xp. 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(.)...,FxP(.) 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(.)...,FxP(.))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.</p

A GLM approach to estimating copula models

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