A GLM Approach to Estimating Copula Models

摘要

Consider the problem of estimating parameter(s) of a copula which provides joint distribution for X-1, X-2, ..., 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 F-X2 (.), F-X3 (.), ... , F-Xp (.) as covariate information about F-X1 (.). Then, it estimates copula's parameter(s) by minimizing mean-squared distance between F-X1 (.) and conditional expectation E(F-X1 (.)vertical bar F-X2 (.), F-X3 (.), ... , F-Xp (.)). 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 Cramer-von Mises distance, compared to other nonparametric estimation methods.