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August 2022 Spectral statistics of high dimensional sample covariance matrix with unbounded population spectral norm
Yanqing Yin
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Bernoulli 28(3): 1729-1756 (August 2022). DOI: 10.3150/21-BEJ1391

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

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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

Information

Received: 1 April 2021; Published: August 2022
First available in Project Euclid: 25 April 2022

Digital Object Identifier: 10.3150/21-BEJ1391

Keywords: large covariance matrix , Linear spectral statistics , spiked eigenvalue , unbounded spectral norm

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Vol.28 • No. 3 • August 2022
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