相依假设下样本相关矩阵最大元的渐近分布

The Asymptotic Distributions of the Largest Entries of Sample Correlation Matrices Under Dependence Assumptions

设{X_(k,i);k≥1,i≥1}是一随机变量组列,令{p_n;n≥1}是一正整数序列,满足c_1≤n/(pn)≤c_2,其中c_1,c_2是正实数.假设{X_(k,i);k≥1,i≥1)满足一些相依条件,得到了L_n的渐近分布,这里■以及■表示(Xi,i...Xn,i)'和(Xi,j...,Xn,j)'间的Pearson相关系数.

Let {Xk,i;k≥1,i≥1} be an array of random variables and let {pn;n≥1} be a sequence of positive integers such that n/pn is bounded away from 0 and∞.Under some dependence assumptions on {Xk,i;k≥1,i≥1},the asymptotic distribution for Ln is obtained,where Ln=max1≤i〈j≤pn｜ ρi,j^（n）｜and ρi,j^（n） denotes the Pearson correlation coefficient between （X1,i,…,Xn,i）′and （X1,j,…,Xn,j）′.