Limit Laws for the Maximum Interpoint Distance under a 1-Dependent Assumption  

作　　者：Haibin ZHANG Yong ZHANG Xue DING 

机构地区：[1]School of Mathematics,Jilin University,Jilin 130012,P.R.China

出　　处：《Journal of Mathematical Research with Applications》2025年第1期105-124,共20页数学研究及应用(英文版)

基　　金：Supported by the National Natural Science Foundation of China(Grant Nos.11771178;12171198);the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC);the Technology Program of Jilin Educational Department During the“14th Five-Year”Plan Period(Grant No.JJKH20241239KJ);the Fundamental Research Funds for the Central Universities.

摘　　要：Let M_(n,p)=(X_(i,k))_(n×p)be an n×p random matrix whose p columns X^((1)),...,X^((p))are an n-dimensional i.i.d.random sample of size p from 1-dependent Gaussian populations.Instead of investigating the special case where p and n are comparable,we consider a much more general case in which log n=o(p^(1/3)).We prove that the maximum interpoint distance Mn=max{|X_(i)-X_(j)|;1≤i<j≤n}converges to an extreme-value distribution,where X_(i)and X_(j)denote the i-th and j-th row of M_(n,p),respectively.The proofs are completed by using the Chen-Stein Poisson approximation method and the moderation deviation principle.

关 键 词：maximum interpoint distance extreme-value distribution Chen-Stein Poisson approximation moderation deviation 1-dependent 

分 类 号：O151.21[理学—数学]