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February 2022 On eigenvalues of a high-dimensional spatial-sign covariance matrix
Weiming Li, Qinwen Wang, Jianfeng Yao, Wang Zhou
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Bernoulli 28(1): 606-637 (February 2022). DOI: 10.3150/21-BEJ1360

Abstract

This paper investigates limiting spectral properties of a high-dimensional sample spatial-sign covariance matrix when both the dimension of the observations and the sample size grow to infinity. The underlying population is general enough to include the popular independent components model and the family of elliptical distributions. The first result of the paper shows that the empirical spectral distribution of a high dimensional sample spatial-sign covariance matrix converges to a generalized Marčenko-Pastur distribution. Secondly, a new central limit theorem for a class of related linear spectral statistics is established.

Acknowledgements

Weiming Li’s research is partially supported by NSFC (No. 11971293) and Program of IRTSHUFE. Qinwen Wang acknowledges support from a NSFC Grant (No. 11801085) and the Shanghai Sailing Program (No. 18YF1401500). Jianfeng Yao’s research is partly supported by a HKSAR RGC Grant (GRF 17306918). Wang Zhou’s research is partially supported by a grant R-155-000-192-114 at the National University of Singapore.

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Weiming Li. Qinwen Wang. Jianfeng Yao. Wang Zhou. "On eigenvalues of a high-dimensional spatial-sign covariance matrix." Bernoulli 28 (1) 606 - 637, February 2022. https://doi.org/10.3150/21-BEJ1360

Information

Received: 1 January 2021; Revised: 1 April 2021; Published: February 2022
First available in Project Euclid: 10 November 2021

Digital Object Identifier: 10.3150/21-BEJ1360

Keywords: central limit theorem , eigenvalue distribution , Linear spectral statistics , spatial-sign covariance matrix

Rights: Copyright © 2022 ISI/BS

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Vol.28 • No. 1 • February 2022
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