On estimation of the spectral measure of certain nonnormal operator stable laws (Q1962234)

A multivariate stable law is parametrized by a triplet \((a, \alpha, \lambda)\) where \(a\in\mathbb{R}^d\) is a location parameter, \(0<\alpha<2\) indicates the tail thickness and \(\lambda\) is a finite Borel measure on the unit sphere; \(\lambda\) is called the spectral measure of \(\nu\) and indicates the dependence structure between the components of a multivariate stable random vector \(X\). For data belonging to the domain of normal attraction of nonormal operator stable laws a strongly consistent estimate of the spectral measure is presented.