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2014 Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models
Wang Qinwen, Su Zhonggen, Yao Jianfeng
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Electron. J. Probab. 19: 1-28 (2014). DOI: 10.1214/EJP.v19-3339

Abstract

In this paper, we derive a joint central limit theorem for random vector whose components are function of random sesquilinear forms. This result is a natural extension of the existing central limit theory on random quadratic forms. We also provide applications in random matrix theory related to large-dimensional spiked population models. For the first application, we find the joint distribution of grouped extreme sample eigenvalues correspond to the spikes. And for the second application, under the assumption that the population covariance matrix is diagonal with $k$ (fixed) simple spikes, we derive the asymptotic joint distribution of the extreme sample eigenvalue and its corresponding sample eigenvector projection.

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Wang Qinwen. Su Zhonggen. Yao Jianfeng. "Joint CLT for several random sesquilinear forms with applications to large-dimensional spiked population models." Electron. J. Probab. 19 1 - 28, 2014. https://doi.org/10.1214/EJP.v19-3339

Information

Accepted: 30 October 2014; Published: 2014
First available in Project Euclid: 4 June 2016

zbMATH: 1307.60017
MathSciNet: MR3275855
Digital Object Identifier: 10.1214/EJP.v19-3339

Subjects:
Primary: 60F05
Secondary: 60B20

Keywords: central limit theorem , Extreme eigenvalues , Extreme eigenvectors , joint distribution , Large-dimensional sample covariance matrices , random quadratic form , Random sesqulinear form , Spiked population model

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