报告题目：Testing covariance structures in commutative quadratic subspace: from fixed to high dimensions

报告人：粱宇莉，广西师范大学

报告时间：2026年10月20日 (星期二) 11:00-11:45

报告地点：伍卓群楼第一报告厅

校内联系方式：邹婷婷[email protected]

报告摘要：

  Commutative quadratic subspaces (CQS) provide a unified framework for covariance structures with known eigenspaces, including compound symmetry and several block models. For fixed dimension, we present likelihood ratio and modified Rao score tests, including an exact null distribution for the likelihood ratio statistic and classical chi-square limits. These null results extend from Gaussian to joint matrix-elliptical models. We also consider a high-dimensional regime in which the dimension (q) and sample size (n) both increase, with (q/n\to c\in[0,\infty)), while the number of spectral components remains fixed. We establish a central limit theorem for the modified Rao score statistic with explicit centering and scaling. As a corollary, its classical chi-square standardization exhibits a limiting mean shift of (c/2).

报告人简介：

  梁宇莉，女，统计学博士，广西师范大学数学与统计博彩App 教师（高层次人才引进）。获瑞典斯德哥尔摩大学统计学博士学位，曾主持瑞典皇家科博彩App G.S. Magnuson 基金青年项目。曾任瑞典国家统计局高级统计师，参与多项瑞典政府官方统计调查的方法设计与数据计算；先后任瑞典厄勒布鲁大学associate senior lecturer（校长战略基金资助的研究型职位）、瑞典林奈大学高级讲师（永久教职）。主要研究方向为含协方差结构的多元模型与高维数据分析，以第一作者或通讯作者在 Journal of Multivariate Analysis、TEST、Biometrical Journal、Statistical Papers 等国际 SCI 期刊发表论文多篇。