Strong convergence of ESD for the generalized sample covariance matrices when

2012 ◽  
Vol 82 (5) ◽  
pp. 894-901 ◽  
Author(s):  
Zhigang Bao
Keyword(s):  
Strong Convergence ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance

Some strong convergence theorems for eigenvalues of general sample covariance matrices

2021 ◽  
Author(s):  
Yanqing Yin
Keyword(s):  
General Population ◽  
Strong Convergence ◽  
Spectral Properties ◽  
Closed Interval ◽  
Open Interval ◽  
Convergence Result ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Class Of Matrices

The aim of this paper is to investigate the spectral properties of sample covariance matrices under a more general population. We consider a class of matrices of the form [Formula: see text], where [Formula: see text] is a [Formula: see text] nonrandom matrix and [Formula: see text] is an [Formula: see text] matrix consisting of i.i.d standard complex entries. [Formula: see text] as [Formula: see text] while [Formula: see text] can be arbitrary but no smaller than [Formula: see text]. We first prove that under some mild assumptions, with probability 1, for all large [Formula: see text], there will be no eigenvalues in any closed interval contained in an open interval which is outside the supports of the limiting distributions for all sufficiently large [Formula: see text]. Then we get the strong convergence result for the extreme eigenvalues as an extension of Bai-Yin law.

Strong convergence of ESD for large quaternion sample covariance matrices and correlation matrices when p/n → 0

2019 ◽  
Vol 09 (02) ◽  
pp. 2050005
Author(s):  
Xue Ding
Keyword(s):  
Strong Convergence ◽  
Sample Size ◽  
Spectral Distribution ◽  
Covariance Matrices ◽  
Correlation Matrices ◽  
Semicircle Law ◽  
Empirical Spectral Distribution ◽  
Sample Covariance Matrices ◽  
Dimension Formula ◽  
Sample Covariance

In this paper, we study the strong convergence of empirical spectral distribution (ESD) of the large quaternion sample covariance matrices and correlation matrices when the ratio of the population dimension [Formula: see text] to sample size [Formula: see text] tends to zero. We prove that the ESD of renormalized quaternion sample covariance matrices converges almost surely to the semicircle law.

scholarly journals On the principal components of sample covariance matrices

2015 ◽  
Vol 164 (1-2) ◽  
pp. 459-552 ◽  
Author(s):  
Alex Bloemendal ◽  
Antti Knowles ◽  
Horng-Tzer Yau ◽  
Jun Yin
Keyword(s):  
Principal Components ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance
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