On the eigenvectors of large-dimensional sample spatial sign covariance matrices

作者：Xu, Yangchang; Xia, Ningning^*

来源：Journal of Multivariate Analysis, 2023, 193: 105119.

DOI：10.1016/j.jmva.2022.105119

• Central limit theorems
• Eigenvectors and eigenvalues
• Haar distribution
• Random matrix
• Spatial sign covariance matrix

To investigate the limiting behavior of eigenvectors of the sample spatial sign covariance matrix (SSCM), the eigenvector empirical spectral distribution (VESD) is defined with weights depending on the eigenvectors. In this paper, we first show that the VESD of a large-dimensional sample SSCM converges to a generalized Marcenko-Pastur distribu-tion when both the dimension p of observations and the sample size n tend to infinity proportionally. Further, the central limit theorem of linear spectral statistics of VESD is established, which suggests that the eigenmatrix of sample SSCM and the classical sample covariance matrix are asymptotically the same.