報(bào)告人：胡江 教授

報(bào)告題目：The Asymptotic Properties of the Extreme Eigenvectors of High-dimensional Generalized Spiked Covariance Model

報(bào)告時(shí)間：2025年5月21日（周三）下午4：30

報(bào)告地點(diǎn)：靜遠(yuǎn)樓1506學(xué)術(shù)報(bào)告廳

主辦單位：數(shù)學(xué)與統(tǒng)計(jì)學(xué)院、數(shù)學(xué)研究院、科學(xué)技術(shù)研究院

報(bào)告人簡(jiǎn)介：

      胡江，東北師范大學(xué)教授，博士生導(dǎo)師，入選“國(guó)家高層次人才特殊支持計(jì)劃”青年拔尖人才。主要從事大維隨機(jī)矩陣?yán)碚撆c大維統(tǒng)計(jì)分析研究，研究興趣包括大維隨機(jī)矩陣特征根與特征向量的極限性質(zhì)、高維估計(jì)與假設(shè)檢驗(yàn)。2012年博士畢業(yè)于東北師范大學(xué)，先后在新加坡國(guó)立大學(xué)、新加坡南洋理工大學(xué)、澳門(mén)大學(xué)、日本廣島大學(xué)、香港科技大學(xué)等學(xué)府訪學(xué)。主持多項(xiàng)國(guó)家自然科學(xué)基金，發(fā)表SCI論文四十余篇，其中包括學(xué)科權(quán)威期刊 The Annals of Statistics等，目前擔(dān)任SCI雜志 Random Matrices: Theory and Applications 主編。

報(bào)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.