Higher-order expansions of distributions of maxima in a Hüsler-Reiss model

Abstract

The max-stable Hüsler-Reiss distribution which arises as the limit distribution of maxima of bivariate Gaussian triangular arrays has been shown to be useful in various extreme value models. For such triangular arrays, this paper establishes higher-order asymptotic expansions of the joint distribution of maxima under refined Hüsler-Reiss conditions. In particular, the rate of convergence of normalized maxima to the Hüsler-Reiss distribution is explicitly calculated.

Convergence rate of maxima of bivariate Gaussian arrays to the Hüsler-Reiss distribution

“…[2] considered the convergence rates of bivariate extreme order statistics under second-order regular varying conditions. For bivariate Hüsler-Reiss Gaussian sequences, recently [6] considered the penultimate and ultimate convergence rate of (n(max 1≤i≤n Φ(ξ ni ) − 1), n(max 1≤i≤n Φ(η ni ) − 1)), and [13] derived the second order expansions of the distribution of normalized M n under the following second order Hüsler-Reiss condition (1.5) lim…”