题目：Spectral properties of rescaled high-dimensional sample correlation matrices

主讲人：东北师范大学 郑术蓉教授

主持人：统计学院 常晋源教授

时间：2021年5月20日（周四）上午10:00-11:00

地点：腾讯会议，552 946 209

报告摘要：

Under the high-dimensional setting that the data dimension and sample size tend to infinity proportionally, we derive the limiting spectral distribution and establish the central limit theorem of eigenvalue statistics of rescaled sample correlation matrices. Distinguished from existing literature, our proposed spectral properties do not require Gaussian distribution assumption or the assumption that the population correlation matrix equals to an identity matrix. The asymptotic mean and variance-covariance in our proposed central limit theorem can be expressed as one-dimensional and two-dimensional contour integrals on a unit circle centered at the origin. Not only is the established central limit theorem of eigenvalue statistics of rescaled sample correlation matrices very different from that of eigenvalue statistics of sample covariance matrices, but also very different from the central limit theorem of eigenvalue statistics of sample correlation matrices with population correlation matrix equalling to an identity matrix. Moreover, to illustrate the spectral properties, we propose three test statistics for the hypothesis testing problem whether the population correlation matrix equals to a given matrix. Furthermore, we conduct extensive simulation studies to investigate the performance of our proposed testing procedures.

主讲人简介：

郑术蓉，东北师范大学教授。主要研究方向是：大维随机矩阵理论及高维统计分析。曾在Annals of Statistics、JASA、Biometrika等统计学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、《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。曾主持国家自然科学基金委优秀青年科学基金、面上项目等多个项目。