Berman’s inequality under random scaling

Abstract

Berman's inequality is the key for establishing asymptotic properties of maxima of Gaussian random sequences and supremum of Gaussian random fields. This contribution shows that, asymptotically an extended version of Berman's inequality can be established for randomly scaled Gaussian random vectors. Two applications presented in this paper demonstrate the use of Berman's inequality under random scaling.

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

“…In fact, the bivariate Hüsler-Reiss distribution appeared in another context in [1], see for recent contribution in this direction [4,17,20,2]. Related results for more general triangular arrays can be found in [9,5,6,8,11,13,14,15,10,3,12]; an interesting statistical applications related to the Hüsler-Reiss distribution is presented in [6].…”

“…In fact, the bivariate Hüsler-Reiss distribution appeared in another context in [1], see for recent contribution in this direction [4,17,20,2]. Related results for more general triangular arrays can be found in [9,5,6,8,11,13,14,15,10,3,12]; an interesting statistical applications related to the Hüsler-Reiss distribution is presented in [6]. For both applications and various theoretical investigations, it is of interest to know how good the Hüsler-Reiss distribution approximates the distribution of the bivariate maxima.…”