Asymptotic properties of type I elliptical random vectors (Q1003307)

Asymptotic expansions are derived for tail probabilities and densities of elliptical random vectors which can be represented in the form \(X=AS\), where \(A\) is a non-singular matrix, and \(S\) is a spherical random vector with Euclidian norm \(| S| \) belonging to the Gumbel domain of max-attraction. The results are applied to the approximation of excess and conditional limiting distributions. Asymptotic distributions of concomitants of order statistics for bivariate elliptical random vectors are derived.