韩潇，中国科学技术大学管理学院特任教授，研究方向为大维随机矩阵；高维统计推断，入选国家创新人才计划青年项目，主持青年基金项目与面上基金项目各一项
In this paper, we introduce the Generalized Linear Spectral Statistics (GLSS) of a high-dimensional sample covariance matrix. The joint asymptotic normality of GLSS associated with different test functions is established when the dimension and the sample size are comparable under weak assumptions. Subsequently, we propose a novel functional projection approach based on GLSS for hypothesis testing on eigenspaces of population-spiked covariance matrices. The theoretical accuracy of our results established for GLSS and the advantages of the newly suggested testing procedure are demonstrated through various numerical studies.
