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20210616:重标度样本相关矩阵的谱特性
时间:2021-06-11

报告时间:2021年6月16日 下午16:00-17:00

报告地点:腾讯会议(会议ID:112 760 451

报告嘉宾:郑术蓉

报告主题:Spectral Properties of Rescaled Sample Correlation Matrix


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.


个人简介

郑术蓉,东北师范大学教授。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学术论文和主持多项国家自然科学基金项目等。现任Statistica Sinica、 Journal of Multivariate Analysis等学术期刊编委。



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