Copulas checker-type approximations: Application to quantiles estimation of sums of dependent random variables

Abstract

Several approximations of copulas have been proposed in the literature. By using empirical versions of checker-type copulas approximations, we propose non parametric estimators of the copula. Under some conditions, the proposed estimators are copulas and their main advantage is that they can be sampled from easily. One possible application is the estimation of quantiles of sums of dependent random variables from a small sample of the multivariate law and a full knowledge of the marginal laws. We show that estimations may be improved by including in an easy way in the approximated copula some additional information on the law of a sub-vector for example. Our approach is illustrated by numerical examples.