On the multivariate Hüsler–Reiss distribution attracting the maxima of elliptical triangular arrays

Abstract

Let ( X 1 n ( j ) , … , X dn ( j ) ) , n ⩾ 1 , 1 ⩽ j ⩽ n , be a triangular array of independent elliptical random vectors in R d , d ⩾ 2 . In this paper we investigate the asymptotic behaviour of the multivariate maxima of this triangular array. Generalising previous results for the bivariate set-up, we show that the normalised maxima of this elliptical triangular array is attracted by the multivariate Hüsler–Reiss distribution function provided that the components of the triangular array become asymptotically dependent with a specific rate, and further the random radius pertaining to the elliptical random vectors is in the Gumbel max-domain of attraction.