报 告 人： 张志翔 博士
报告题目：Asymptotic Independence of Spiked Eigenvalus and Linear Spectral Statistics For Large Sample Covariance Matrices
We consider a general spiked sample covariance model and prove a central limit theorem of spiked eigenvalues under the regime that the dimension and sample size grow to infinityproportionally.This result is an extension of previous central limit theorem established forspiked eigenvalues under the assumption that the population covariance matrix has a blockdiagonal structure. Another main theoretical result of our work is about the relationship between spiked eigenvalues and linear spectral statistics. We show that they are asymptotically independent. Based on these results, we propose a statistic to test equality of twospiked population covariance matrices. Some corrected consistent estimators of spikedpopulation eigenvectors are also proposed for application.