Maxima of a triangular array of multivariate Gaussian sequence

It is known that the normalized maxima of a sequence of independent and identically distributed bivariate normal random vectors with correlation coefficient ρ∈[−1,1)ρ∈[−1,1) is asymptotically independent, which implies that using bivariate normal distribution will seriously underestimate extreme co-movement in practice. By letting ρρ depend on the sample size and go to one with certain rate, Hüsler and Reiss (1989) showed that the normalized maxima of Gaussian random vectors can become asymptotically dependent so as to well predict the co-movement observed in the market. In this paper, we extend such a study to a triangular array of a multivariate Gaussian sequence, which further generalizes the results in Hsing et al. (1996) and Hashorva and Weng (2013).