Central Limit Theorem of Linear Spectral Statistics of Large Dimensional Sample Correlation Matrices
数学公众报告（120 周年校庆系列第2场）
报告题目(Title)：Central Limit Theorem of Linear Spectral Statistics of Large Dimensional Sample Correlation Matrices
报告人(Speaker)：郑术蓉教授（东北师范大学）
地点(Place)：腾讯会议 会议ID：545 825 666
时间(Time)：2021年12月03日 周五 14:00-15:00
邀请人(Inviter)：何辉
报告摘要
Under the high-dimensional setting that the dimension tends to infinity proportionally with the sample size, we establish the central limit theorems (CLT) for linear spectral statistics (LSS) of sample correlation matrices under two settings: (1). The population follows an independent component structure; (2). The population follows an elliptical structure. It shows that the CLTs of LSS of sample correlation matrices are very different under the two settings. Especially, even if the population correlation matrix is an identity matrix, the CLTs are different under the two settings. An application of our established two CLTs is given.
主讲人简介
郑术蓉，东北师范大学教授，博士生导师。主要从事大维随机矩阵理论及高维统计分析的研究。曾在Annals of Statistics, JASA, Biometrika等统计学重要学术期刊上发表多篇跟大维随机矩阵理论有关的学术论文。现任Statistica Sinica、 Journal of Multivariate Analysis、Statistics & Probability Letters、《应用概率统计》学术期刊编委，全国青年统计学家协会副会长等，曾主持多项国家自然科学基金项目等。
