THE EXTREMES OF A TRIANGULAR ARRAY OF NORMAL RANDOM VARIABLES
成果类型：
Article
署名作者：
Hsing, Tailen; Husler, Jurg; Reiss, Rolf-Dieter
署名单位：
Texas A&M University System; Texas A&M University College Station; University of Bern; Universitat Siegen
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
1996
页码：
671-686
关键词：
摘要：
Consider a triangular array of stationary normal random variables {xi(n,i), i >= 0, n >= 1} such that {xi(n,i), i >= 0} is a stationary normal sequence for each n >= 1. Let p(n,j) = corrq{xi(n,i), xi(n,i), (i + j) ). We show that if (1 - p(n),(j))log n -> delta(j) is an element of (0, infinity) as n -> infinity for some j, then the locations where the extreme values occur cluster, and if p(n,j) tends to 0 fast enough as j -> infinity for fixed n, then {xi(n,i), i >= 0} satisfies a certain weak dependence condition. Under the two conditions, it is possible to speak about an index which measures the degree of clustering. In practice, this viewpoint can provide a better approximation of the distributions of the maxima of weakly dependent normal random variables than what is directly guided by the asymptotic theory of Berman.