Generalized Linear Spectral Statistics of High-dimensional Sample Covariance Matrices and Its Applications
报告人： 韩潇（中国科学技术大学管理学院）
时间：2026-10-29 13:30-14:50
地点：Room 217, Guanghua Building 2
Abstract:
We investigate generalized linear spectral statistics (GLSS) for a high-dimensional sample covariance matrix Sₙ, defined by tr[f(Sₙ)Bₙ]. The inclusion of an auxiliary matrix Bₙ and a test function f allows these statistics to describe different spectral features of Sₙ.
When the dimension n and sample size N are of comparable orders, we establish joint asymptotic normality for GLSS corresponding to multiple test functions under mild assumptions on Bₙ and the underlying distribution. The convergence rate is governed by √(N/rank(Bₙ)).
Building on these results, we develop a functional-projection approach for testing eigenspaces in population-spiked covariance models and identify a universality phenomenon concerning spike magnitudes. Numerical experiments support the theoretical findings and demonstrate the advantages of the proposed testing procedure.
About the Speaker:
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。
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