報告人：胡江 教授

報告題目：The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized Spiked Covariance Model

報告時間：2025年5月21日（周三）下午4：30

報告地點：靜遠樓1506學術報告廳

主辦單位：數(shù)學與統(tǒng)計學院、數(shù)學研究院、科學技術研究院

報告人簡介：

      胡江，東北師范大學教授，博士生導師，入選“國家高層次人才特殊支持計劃”青年拔尖人才。主要從事大維隨機矩陣理論與大維統(tǒng)計分析研究，研究興趣包括大維隨機矩陣特征根與特征向量的極限性質(zhì)、高維估計與假設檢驗。2012年博士畢業(yè)于東北師范大學，先后在新加坡國立大學、新加坡南洋理工大學、澳門大學、日本廣島大學、香港科技大學等學府訪學。主持多項國家自然科學基金，發(fā)表SCI論文四十余篇，其中包括學科權威期刊 The Annals of Statistics等，目前擔任SCI雜志 Random Matrices: Theory and Applications 主編。

報告摘要：

               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.