Second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization

TL;DR

This paper investigates second order expansions of the distribution of maxima in bivariate Gaussian triangular arrays under power normalization, comparing these to linear normalization results to understand their asymptotic behaviors.

Contribution

It provides new second order expansion results for maxima distributions under power normalization, extending previous linear normalization analyses.

Findings

Second order expansions differ significantly from linear normalization cases.

Numerical analyses illustrate the asymptotic differences between power and linear normalization.

Results enhance understanding of the tail behavior of maxima in Gaussian arrays.

Abstract

In this paper, we study second order expansions of distributions of maxima of bivariate Gaussian triangular arrays under power normalization. Numerical analysis are given to compare the asymptotic behaviors under power normalization with the asymptotic behaviors under linear normalization derived by Hashorva et al. (2016).