ASYMPTOTIC NORMALITY FOR EIGENVALUE STATISTICS OF A GENERAL SAMPLE COVARIANCE MATRIX WHEN p/n? 8 AND APPLICATIONS

• 成果类型: Article
• 署名作者: Qiu, Jiaxin; Li, Zeng; Yao, Jianfeng
• 署名单位: University of Hong Kong; Southern University of Science & Technology; The Chinese University of Hong Kong, Shenzhen
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/23-AOS2300
• 发表日期: 2023
• 页码: 1427-1451
• 关键词: linear spectral statistics; CONVERGENCE; dimension; sphericity; larger; clt

摘要

The asymptotic normality for a large family of eigenvalue statistics of a general sample covariance matrix is derived under the ultrahigh-dimensional setting, that is, when the dimension to sample size ratio p/n & RARR; & INFIN;. Based on this CLT result, we extend the covariance matrix test problem to the new ultra-high-dimensional context, and apply it to test a matrix-valued white noise. Simulation experiments are conducted for the investigation of finite-sample properties of the general asymptotic normality of eigenvalue statistics, as well as the two developed tests.