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

Let {(ξ_ni, η_ni), 1 ≤ i ≤ n, n ≥ 1} be a triangular array of independent bivariate elliptical random vectors with the same distribution function as (S1,ρnS1+1−ρn2S2),ρn∈(0,1)<inline-graphic></inline-graphic>, where (S¹, S₂) is a bivariate spherical random vector. For the distribution function of radius S12+S22<inline-graphic></inline-graphic> 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 ρ_n to 1 is given. In this paper, under the refinement of the rate of convergence of ρ_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. [ABSTRACT FROM AUTHOR]