Second-order Asymptotics on Distributions of Maxima of Bivariate Elliptical Arrays

Let {(. ni , . ni ), 1 . i . n, n . 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as (S1,.nS1+1..2n......S2),.n.(0,1), where (S1, S2) is a bivariate spherical random vector. For the distribution function of radius S21+S22........ belonging to the max-domain of attraction of the Weibull distribution, the limiting distribution of maximum of this triangular array is known as the convergence rate of . n to 1 is given. In this paper, under the refinement of the rate of convergence of . n to 1 and the second-order regular variation of the distributional tail of radius, precise second-order distributional expansions of the normalized maxima of bivariate elliptical triangular arrays are established.