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.
翻译:通常提议使用多电子相交合体来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。当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时,当它不属于一个参数组时,对密度生成器则不如此。我们说明非参数识别该生成器的充分条件。然后,通过M-估计、模拟推论或R包中的迭接程序提出若干非参数估计值$g$。一些模拟说明了后一种方法的相关性。