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December 2020 Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model
Zeng Li, Fang Han, Jianfeng Yao
Ann. Statist. 48(6): 3138-3160 (December 2020). DOI: 10.1214/19-AOS1882

Abstract

This paper studies the joint limiting behavior of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model, where the asymptotic regime is such that the dimension and sample size grow proportionally. The form of the joint limiting distribution is applied to conduct Johnson–Graybill-type tests, a family of approaches testing for signals in a statistical model. For this, higher order correction is further made, helping alleviate the impact of finite-sample bias. The proof rests on determining the joint asymptotic behavior of two classes of spectral processes, corresponding to the extreme and linear spectral statistics, respectively.

Citation

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Zeng Li. Fang Han. Jianfeng Yao. "Asymptotic joint distribution of extreme eigenvalues and trace of large sample covariance matrix in a generalized spiked population model." Ann. Statist. 48 (6) 3138 - 3160, December 2020. https://doi.org/10.1214/19-AOS1882

Information

Received: 1 September 2018; Revised: 1 June 2019; Published: December 2020
First available in Project Euclid: 11 December 2020

MathSciNet: MR4185803
Digital Object Identifier: 10.1214/19-AOS1882

Subjects:
Primary: 62E20, 62H15
Secondary: 15B52

Rights: Copyright © 2020 Institute of Mathematical Statistics

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Vol.48 • No. 6 • December 2020
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