报告题目：Spectral analysis of spatial-sign covariance matrices with dependence and weaker moment conditions

报告人：王成

时间：2026年5月18日星期一10：00—11：00

地点：动漫a片 106会议室

摘要：This talk investigates the spectral properties of spatial-sign covariance matrices, a self-normalized version of sample covariance matrices, for data from $\alpha$-regularly varying populations with general covariance structures. By exploiting the elegant properties of self-normalized random variables, we establish the limiting spectral distribution and a central limit theorem for linear spectral statistics. We demonstrate that the Mar{\u{c}}enko-Pastur equation holds under the condition $\alpha \geq 2$, while the central limit theorem for linear spectral statistics is valid for $\alpha>4$, which are shown to be nearly the weakest possible conditions for spatial-sign covariance matrices from heavy-tailed data in the presence of dependence.

专家简介：王成，上海交通⼤学数学科学学院长聘副教授，博士生导师。2013年博士毕业于中国科学技术⼤学，主要研究⽅向为随机矩阵理论及应⽤、⾼维数据分析等。在统计领域核⼼期刊Statistica Sinica, Science China Mathematics等发表学术论⽂三十余篇。先后主持国家⾃然科学基⾦青年基金、面上项目2项、上海市科研项⽬2项，参与国家⾃然科学基⾦重大项目和重点项⽬。曾获得过中科院院⻓特别奖，上海交大教书育人三等奖等荣誉。