Please use this identifier to cite or link to this item: https://hdl.handle.net/10356/80954
Title: Convergence of the empirical spectral distribution function of Beta matrices
Authors: Bai, Zhidong
Hu, Jiang
Pan, Guangming
Zhou, Wang
Keywords: Beta matrices
CLT
LSD
Multivariate statistical analysis
Issue Date: 2015
Source: Bai, Z., Hu, J., Pan, G., & Zhou, W. (2015). Convergence of the empirical spectral distribution function of Beta matrices. Bernoulli, 21(3), 1538-1574.
Series/Report no.: Bernoulli
Abstract: 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.
URI: https://hdl.handle.net/10356/80954
http://hdl.handle.net/10220/38995
ISSN: 1350-7265
DOI: 10.3150/14-BEJ613
Schools: School of Physical and Mathematical Sciences 
Rights: © 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.
Fulltext Permission: open
Fulltext Availability: With Fulltext
Appears in Collections:SPMS Journal Articles

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