Estimation of a Copula when a Covariate Affects only Marginal Distributions

Irène Gijbels, Marek Omelka and Noël Veraverbeke

Scandinavian Journal of Statistics, 2015, vol. 42, issue 4, 1109-1126

Abstract: type="main" xml:id="sjos12154-abs-0001"> This paper is concerned with studying the dependence structure between two random variables Y 1 and Y 2 in the presence of a covariate X, which affects both marginal distributions but not the dependence structure. This is reflected in the property that the conditional copula of Y 1 and Y 2 given X, does not depend on the value of X. This latter independence often appears as a simplifying assumption in pair-copula constructions. We introduce a general estimator for the copula in this specific setting and establish its consistency. Moreover, we consider some special cases, such as parametric or nonparametric location-scale models for the effect of the covariate X on the marginals of Y 1 and Y 2 and show that in these cases, weak convergence of the estimator, at n -rate, holds. The theoretical results are illustrated by simulations and a real data example.

Date: 2015
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