A GLM Approach to Estimating Copula Models

Abstract

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 as covariate information about Then, it estimates copula’s parameter(s) by minimizing mean-squared distance between and conditional expectation 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, Kendal’s tau, Spearman’s 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.

Keywords:

• Copula
• GLM
• Parameter estimation
• Quantile regression 2010

Mathematics Subject Classification:

• 62F10
• 62J05
• 62J12
• 62H20