91九色

为促进学科交流融合、拓宽师生学术视野、释放科研创新活力，助力人大数学学科走向一流，91九色 设立“人大数学时间”，以专题研讨、高端学术论坛为载体，搭建数学思想充分碰撞、优秀人才不断涌流、创造活力竞相迸发的舞台。“人大数学时间”将持之以恒，久久为功，立志通过交流与创新、提出重大问题，引领数学学科及相关领域的创新与发展，成为对我国数学发展有贡献意义的平台。以下为“人大数学时间I”第三十六期信息：

议程：

    时间：11月28日（星期五）15：00 

    郑术蓉教授报告及前沿问题探讨

地点：立德楼503

线上：腾讯会议：402-698-950

题目：Spectral Properties of High-dimensional Rescaled Sample Correlation Matrices

主讲专家：郑术蓉，东北师范大学教授

摘要：

High-dimensional sample correlation matrices are a crucial class of random matrices in multivariate statistical analysis. The central limit theorem (CLT) provides a theoretical foundation for statistical inference. In this paper, assuming that the data dimension increases proportionally with the sample size, we derive the limiting spectral distribution of the matrix RM and establish its CLTs for the linear spectral statistics (LSS) in two structures: linear independent component structure and elliptical structure. In contrast to the existing literature, our proposed spectral properties do not require M to be an identity matrix. Moreover, we also derive the joint limiting distribution of LSSs of RM1,…,RMK. As an illustration, an application is given for the CLT.

报告人简介：

郑术蓉，东北师范大学教授，国家级高层次人才，主要研究方向为大维随机矩阵理论及其应用。相关研究成果发表在Annals of Statistics、Journal of the American Statistical Association、Biometrika、Bernoulli等学术期刊上。现任Statistica Sinica, Journal of Business & Economic Statistics, Journal of Multivariate Analysis等多个学术期刊编委。