Generalized simulated method-of-moments estimators for multivariate copulas

This paper introduces a general semi-parametric method for estimating a vector of parameters in multivariate copula models. The proposed approach uses the moments of the multivariate probability integral random variable to generalize the inversion of Kendall's tau estimator. What makes the new methodology attractive is the fact that it can be performed as soon as one can simulate from the assumed parametric family of copulas. This feature is especially helpful when explicit expressions are not available for the theoretical moments. The consistency and asymptotic normality of the proposed estimators are established under mild conditions. An extensive simulation study indicates that the price to pay for the estimation of the moments is modest and that the new estimators are almost as accurate as the pseudo-maximum likelihood (PML) estimator. The usefulness of the proposed estimators is illustrated on the modelling of multivariate data with copula models where the PML estimator is hardly computable.