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February 2019 High-dimensional covariance matrices in elliptical distributions with application to spherical test
Jiang Hu, Weiming Li, Zhi Liu, Wang Zhou
Ann. Statist. 47(1): 527-555 (February 2019). DOI: 10.1214/18-AOS1699


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.


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Jiang Hu. Weiming Li. Zhi Liu. Wang Zhou. "High-dimensional covariance matrices in elliptical distributions with application to spherical test." Ann. Statist. 47 (1) 527 - 555, February 2019.


Received: 1 January 2017; Revised: 1 October 2017; Published: February 2019
First available in Project Euclid: 30 November 2018

zbMATH: 07036210
MathSciNet: MR3909941
Digital Object Identifier: 10.1214/18-AOS1699

Primary: 62H15
Secondary: 62H10

Keywords: Covariance matrix , elliptical distribution , High-dimensional data , sphericity test

Rights: Copyright © 2019 Institute of Mathematical Statistics


Vol.47 • No. 1 • February 2019
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