题    目：The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized           Spiked Covariance Model

主讲人：胡江 教授

单    位：东北师范大学

时    间：2025年12月2日 10:00

腾讯ID：193-663-439

摘    要：In this talk, 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 non-spiked ones. Finally, we propose a powerful statistic for hypothesis testing for the eigenspaces of covariance matrices.

简    介：胡江，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。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。