The Asymptotic Distributions of the Largest Entries of Sample Correlation Matrices under an α-mixing Assumption  

作　　者：Hao Zhu ZHAO Yong ZHANG 

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

出　　处：《Acta Mathematica Sinica,English Series》2022年第11期2039-2056,共18页数学学报（英文版）

基　　金：National Natural Science Foundation of China(Grant Nos.11771178 and 12171198);the Science and Technology Development Program of Jilin Province(Grant No.20210101467JC);Science and Technology Program of Jilin Educational Department during the“13th Five-Year”Plan Period(Grant No.JJKH20200951KJ);Fundamental Research Funds for the Central Universities。

摘　　要：Let{Xk,i;k≥1,i≥1}be an array of random variables,{Xk;k≥1}be a strictly stationaryα-mixing sequence,where Xk=(Xk,1,Xk,2,...).Let{pn;n≥1}be a sequence of positive integers such that c1≤p n n≤c2,where c1,c2>0.In this paper,we obtain the asymptotic distributions of the largest entries Ln=max1≤i<j≤pn|ρ(n)ij|of the sample correlation matrices,whereρ(n)ij denotes the Pearson correlation coefficient between X(i)and X(j),X(i)=(X1,i,X2,i,...).The asymptotic distributions of Ln is derived by using the Chen–Stein Poisson approximation method.

关 键 词：Sample correlation matrices α-mixing sequence Chen-Stein method 

分 类 号：O212.1[理学—概率论与数理统计]