ASYMPTOTIC JOINT DISTRIBUTION OF EXTREME EIGENVALUES AND TRACE OF LARGE SAMPLE COVARIANCE MATRIX IN A GENERALIZED SPIKED POPULATION MODEL

• 成果类型: Article
• 署名作者: Li, Zeng; Han, Fang; Yao, Jianfeng
• 署名单位: Southern University of Science & Technology; University of Washington; University of Washington Seattle; University of Hong Kong
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/19-AOS1882
• 发表日期: 2020
• 页码: 3138-3160
• 关键词: linear spectral statistics; central limit-theorems; clt; components; eigenstructure; number; tests

摘要

This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow proportionally. The form of the joint limiting distribution is applied to conduct Johnson-Graybill-type tests, a family of approaches testing for signals in a statistical model. For this, higher order correction is further made, helping alleviate the impact of finite-sample bias. The proof rests on determining the joint asymptotic behavior of two classes of spectral processes, corresponding to the extreme and linear spectral statistics, respectively.