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.
翻译:常提议模拟随机矢量各组成部分之间的依赖性。它们由相关矩阵和地图($g$)加以说明,称为密度生成器。虽然后者的关联矩阵可以很容易地从观测的伪样本中估算出来,但密度生成器更难估计,特别是当它不属于参数组时。我们给非参数识别该生成器提供了充分的条件。然后,通过M-估计、模拟推论或R包件 ElliptCopulas 中可用的迭接程序,提出了若干非参数估算值$g$。一些模拟显示了后一种方法的相关性。