Estimation in copula models with two-piece skewed margins using the inference for margins method

Abstract

Copulas provide a versatile tool in the modelling of multivariate distributions. With an increased awareness for possible asymmetry in data, skewed copulas in combination with classical margins have been employed to appropriately model these data. The reverse, skewed margins with a (classical) copula has also been considered, but mainly with classical skew-symmetrical margins. An alternative approach is to rely on a large family of asymmetric two-piece distributions for the univariate marginal distributions. Together with any copula this family of asymmetric univariate distributions provides a powerful tool for skewed multivariate distributions. Maximum likelihood estimation of all parameters involved is discussed. A key step in achieving statistical inference results is an extension of the theory available for generalized method of moments, under non-standard conditions. This together with the inference results for the family of univariate distributions, allows to establish consistency and asymptotic normality of the estimators obtained through the method of ‘inference functions for margins’. The theoretical results are complemented by a simulation study and the practical use of the method is demonstrated on real data examples.