HIGH-DIMENSIONAL COVARIANCE MATRICES IN ELLIPTICAL DISTRIBUTIONS WITH APPLICATION TO SPHERICAL TEST

• 成果类型: Article
• 署名作者: Hu, Jiang; Li, Weiming; Liu, Zhi; Zhou, Wang
• 署名单位: Northeast Normal University - China; Northeast Normal University - China; Shanghai University of Finance & Economics; University of Macau; National University of Singapore
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/18-AOS1699
• 发表日期: 2019
• 页码: 527-555
• 关键词: empirical distribution; Spectral Distribution; principal components; LARGEST EIGENVALUE; limit; CONVERGENCE

摘要

This paper discusses fluctuations of linear spectral statistics of high-dimensional sample covariance matrices when the underlying population follows an elliptical distribution. Such population often possesses high order correlations among their coordinates, which have great impact on the asymptotic behaviors of linear spectral statistics. Taking such kind of dependency into consideration, we establish a new central limit theorem for the linear spectral statistics in this paper for a class of elliptical populations. This general theoretical result has wide applications and, as an example, it is then applied to test the sphericity of elliptical populations.