Abstract
In this paper, we establish some new central limit theorems for certain spectral statistics of a high-dimensional sample covariance matrix under a divergent spectral norm population model. This model covers the divergent spiked population model as a special case. Meanwhile, the number of the spiked eigenvalues can either be fixed or grow to infinity. It is seen from our theorems that the divergence of population spectral norm affects the fluctuations of the linear spectral statistics in a fickle way, depending on the divergence rate.
Funding Statement
Yanqing Yin is supported by a project of NSFC grant 11801234.
Acknowledgments
The author would like to thank Prof. Weiming Li for his constructive suggestions on the organization of this paper. Moreover, the author thank the associate editor, referees, and editor for their constructive feedback and helpful comments.
Citation
Yanqing Yin. "Spectral statistics of high dimensional sample covariance matrix with unbounded population spectral norm." Bernoulli 28 (3) 1729 - 1756, August 2022. https://doi.org/10.3150/21-BEJ1391
