Asymptotics and statistical inferences on independent and non-identically distributed bivariate Gaussian triangular arrays

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In this paper, we establish the first and the second-order asymptotics of distributions of normalized maxima of independent and non-identically distributed bivariate Gaussian triangular arrays, where each vector of the nth row follows from a bivariate Gaussian distribution with correlation coefficient being a monotone continuous function of i/n. Furthermore, parametric inference for this unknown function is studied. Some simulation study and real data sets analysis are also presented.