Multivariate and functional covariates and conditional copulas

Abstract

In this paper the interest is to estimate the dependence between two variables conditionally upon a covariate, through copula modelling. In recent literature nonparametric estimators for conditional copula functions in case of a univariate covariate have been proposed. The aim of this paper is to nonparametrically estimate a conditional copula when the covariate takes on values in more complex spaces. We consider multivariate covariates and functional covariates. We establish weak convergence, and bias and variance properties of the proposed nonparametric estimators. We also briefly discuss nonparametric estimation of conditional association measures such as a conditional Kendalls tau. The case of functional covariates is of particular interest and challenge, both from theoretical as well as practical point of view. For this setting we provide an illustration with a real data example in which the covariates are spectral curves. A simulation study investigating the finite-sample performances of the discussed estimators is provided.