Identifiability and estimation of meta-elliptical copula generators

TL;DR

This paper investigates how to non-parametrically identify and estimate the density generator of meta-elliptical copulas, providing theoretical conditions and practical estimators, including an R package implementation.

Contribution

It offers sufficient conditions for non-parametric identification of the generator and introduces new estimators, including an iterative method implemented in R.

Findings

The iterative estimator performs well in simulations.

Non-parametric identification is feasible under certain conditions.

The R package ElliptCopulas facilitates practical estimation.

Abstract

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 density generator. While the latter correlation matrix can easily be estimated from pseudo-samples of observations, the density generator is harder to estimate, especially when it does not belong to a parametric family. We give 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 the R package ElliptCopulas. Some simulations illustrate the relevance of the latter method.