报告人：胡江 教授
报告题目：The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized Spiked Covariance Model
报告时间：2025年5月21日（周三）下午4：30
报告地点：静远楼1506学术报告厅
主办单位：数学与统计学院、数学研究院、科学技术研究院
报告人简介：
胡江，东北师范大学教授，博士生导师，入选“国家高层次人才特殊支持计划”青年拔尖人才。主要从事大维随机矩阵理论与大维统计分析研究，研究兴趣包括大维随机矩阵特征根与特征向量的极限性质、高维估计与假设检验。2012年博士毕业于东北师范大学，先后在新加坡国立大学、新加坡南洋理工大学、澳门大学、日本广岛大学、香港科技大学等学府访学。主持多项国家自然科学基金，发表SCI论文四十余篇，其中包括学科权威期刊 The Annals of Statistics等，目前担任SCI杂志 Random Matrices: Theory and Applications 主编。
报告摘要：
In this paper, we investigate the asymptotic behaviors of the extreme eigenvectors in a general spiked covariance matrix, where the dimension and sample size increase proportionally. We eliminate the restrictive assumption of the block diagonal structure in the population covariance matrix. Moreover, there is no requirement for the spiked eigenvalues and the 4th moment to be bounded. Specifically, we apply random matrix theory to derive the convergence and limiting distributions of certain projections of the extreme eigenvectors in a large sample covariance matrix within a generalized spiked population model. Furthermore, our techniques are robust and effective, even when spiked eigenvalues differ significantly in magnitude from nonspiked ones. Finally, we propose a powerful statistic for hypothesis testing for the eigenspaces of covariance matrices.