12月12日 张志翔博士学术报告(数学与统计学院)

威尼斯人游戏网站:2019-12-11浏览:91设置

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

报告威尼斯人游戏网站:2019年12月12日(周四)上午10:20

报告地点:静远楼1508学术报告厅

主办单位:数学与统计学院、科学技术研究院

报告摘要:

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.


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