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.I...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.展开更多
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)+1 种基金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。
文摘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.