报 告 人：郑术蓉 教授
报告题目：Large separable sample covariance matrices: joint CLT for linear spectral statistics and its applications
报告时间：2023年10月14日（周六上午9：30 )
报告地点：华体会平台数学与统计学院学术报告厅（静远楼1506室）
主办单位：数学研究院、数学与统计学院、科学技术研究院
报告人简介：
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Annals of Statistics、Statistica Sinica、Journal of Multivariate Analysis等学术期刊编委。
报告摘要：
This paper studies a group of correlated separable sample covariance matrices which share a latent random matrix but have distinct spatial-temple covariance structures. The entries of the random matrix can be either independent and identically distributed or elliptically correlated across rows. A joint central limit theorem for linear spectral statistics of such covariance matrices is established in high-dimensional frameworks. By utilizing this general result, we extend two classical likelihood ratio tests to high-dimensional situations, including the significance test in a multivariate linear regression and the test for the equality of several covariance matrices.