Identifiability and estimation of meta-elliptical copula generators

Meta-elliptical copulas are often proposed to model dependence between the components of a random vector. They are specified by a correlation matrix and a map $g$, called a density generator. When the latter correlation matrix can easily be estimated from pseudo-samples of observations, this is not the case for the density generator when it does not belong to a parametric family. We state sufficient conditions to non-parametrically identify this generator. Several nonparametric estimators of $g$ are then proposed, by M-estimation, simulation-based inference or by an iterative procedure available in a R package. Some simulations illustrate the relevance of the latter method.