Maxima and minima of independent and non-identically distributed bivariate Gaussian triangular arrays

TL;DR

This paper derives the joint limit distributions of maxima and minima in non-identically distributed bivariate Gaussian arrays, including second-order expansions under certain conditions, advancing understanding of their asymptotic behavior.

Contribution

It introduces new results on joint limit distributions and second-order expansions for maxima and minima in non-i.i.d. bivariate Gaussian arrays with correlation functions depending on index ratios.

Findings

Joint limit distributions of maxima and minima are derived.

Second-order expansions are established under regular conditions.

Results extend classical extreme value theory to non-i.i.d. Gaussian arrays.

Abstract

In this paper, joint limit distributions of maxima and minima on independent and non-identically distributed bivariate Gaussian triangular arrays is derived as the correlation coefficient of $i$th vector of given $n$th row is the function of $i/n$. Furthermore, second-order expansions of joint distributions of maxima and minima are established if the correlation function satisfies some regular conditions.