2012/02/28_Noel Veraverbeke (University of Hasselt, Belgium)

Copulas and covariates

2012/02/28 – 14:00 h | Noel Veraverbeke, University of Hasselt (Belgium).

Abstract

Studying the relationship between two (or more) random variables in the presence of a covariate can be done based on a conditional version of Sklar’s theorem: there exists a copula function expressing the joint conditional distribution as a function of the one dimensional conditional marginal distributions. We discuss recent results on several estimators for this unknown copula function. First of all there is the nonparametric method which uses empirical estimators with weights that smooth over the covariate space. An application is the asymptotic theory for asso- ciation measures like the conditional Kendall’s tau. A second method is semi-parametric in nature: it starts from a parametric family of copulas in which the parameter depends on the covariate. This parameter function is estimated by local likelihood. A third method provides a smooth estimator by the use of Bernstein polynomials.