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 spe...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.展开更多
基金Supported by the National Natural Science Foundation of China(Grant Nos.1177117812171198)+2 种基金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.
文摘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.
