Convergence of the empirical spectral distribution function of Beta matrices

Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral sta...

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Main Authors:	Bai, Zhidong, Hu, Jiang, Pan, Guangming, Zhou, Wang
Other Authors:	School of Physical and Mathematical Sciences
Format:	Article
Language:	English
Published:	2015
Subjects:	Beta matrices CLT LSD Multivariate statistical analysis
Online Access:	https://hdl.handle.net/10356/80954 http://hdl.handle.net/10220/38995
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Institution:	Nanyang Technological University
Language:	English

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spelling	sg-ntu-dr.10356-809542023-02-28T19:22:14Z Convergence of the empirical spectral distribution function of Beta matrices Bai, Zhidong Hu, Jiang Pan, Guangming Zhou, Wang School of Physical and Mathematical Sciences Beta matrices CLT LSD Multivariate statistical analysis Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral statistics of Bn. Especially, we do not require Sn or TN to be invertible. Namely, we can deal with the case where p>max{n,N} and p<n+N. Therefore, our results cover many important applications which cannot be simply deduced from the corresponding results for multivariate F matrices. Published version 2015-12-08T02:56:46Z 2019-12-06T14:18:13Z 2015-12-08T02:56:46Z 2019-12-06T14:18:13Z 2015 Journal Article Bai, Z., Hu, J., Pan, G., & Zhou, W. (2015). Convergence of the empirical spectral distribution function of Beta matrices. Bernoulli, 21(3), 1538-1574. 1350-7265 https://hdl.handle.net/10356/80954 http://hdl.handle.net/10220/38995 10.3150/14-BEJ613 en Bernoulli © 2015 Bernoulli Society for Mathematical Statistics and Probability. This paper was published in Bernoulli and is made available as an electronic reprint (preprint) with permission of Bernoulli Society for Mathematical Statistics and Probability. The published version is available at: [http://dx.doi.org/10.3150/14-BEJ613]. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law. 37 p. application/pdf
institution	Nanyang Technological University
building	NTU Library
continent	Asia
country	Singapore Singapore
content_provider	NTU Library
collection	DR-NTU
language	English
topic	Beta matrices CLT LSD Multivariate statistical analysis
spellingShingle	Beta matrices CLT LSD Multivariate statistical analysis Bai, Zhidong Hu, Jiang Pan, Guangming Zhou, Wang Convergence of the empirical spectral distribution function of Beta matrices
description	Let Bn=Sn(Sn+αnTN)−1, where Sn and TN are two independent sample covariance matrices with dimension p and sample sizes n and N, respectively. This is the so-called Beta matrix. In this paper, we focus on the limiting spectral distribution function and the central limit theorem of linear spectral statistics of Bn. Especially, we do not require Sn or TN to be invertible. Namely, we can deal with the case where p>max{n,N} and p<n+N. Therefore, our results cover many important applications which cannot be simply deduced from the corresponding results for multivariate F matrices.
author2	School of Physical and Mathematical Sciences
author_facet	School of Physical and Mathematical Sciences Bai, Zhidong Hu, Jiang Pan, Guangming Zhou, Wang
format	Article
author	Bai, Zhidong Hu, Jiang Pan, Guangming Zhou, Wang
author_sort	Bai, Zhidong
title	Convergence of the empirical spectral distribution function of Beta matrices
title_short	Convergence of the empirical spectral distribution function of Beta matrices
title_full	Convergence of the empirical spectral distribution function of Beta matrices
title_fullStr	Convergence of the empirical spectral distribution function of Beta matrices
title_full_unstemmed	Convergence of the empirical spectral distribution function of Beta matrices
title_sort	convergence of the empirical spectral distribution function of beta matrices
publishDate	2015
url	https://hdl.handle.net/10356/80954 http://hdl.handle.net/10220/38995
_version_	1759857991658504192

Convergence of the empirical spectral distribution function of Beta matrices

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