scholarly journals On asymptotic expansion and CLT of linear eigenvalue statistics for sample covariance matrices when $N/M\rightarrow0$

2014 ◽  
Vol 59 (2) ◽  
pp. 313-339
Author(s):  
Z Bao ◽  
Z Bao
Keyword(s):  
Asymptotic Expansion ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Linear Eigenvalue Statistics ◽  
Sample Covariance ◽  
Eigenvalue Statistics

Fluctuations for differences of linear eigenvalue statistics for sample covariance matrices

2019 ◽  
Vol 09 (03) ◽  
pp. 2050006 ◽  
Author(s):  
Giorgio Cipolloni ◽  
László Erdős
Keyword(s):  
Covariance Matrices ◽  
Gaussian Field ◽  
Linear Statistics ◽  
Sample Covariance Matrices ◽  
Linear Eigenvalue Statistics ◽  
Sample Covariance ◽  
Eigenvalue Statistics ◽  
Matrix Formula ◽  
The Difference ◽  
The Individual

We prove a central limit theorem for the difference of linear eigenvalue statistics of a sample covariance matrix [Formula: see text] and its minor [Formula: see text]. We find that the fluctuation of this difference is much smaller than those of the individual linear statistics, as a consequence of the strong correlation between the eigenvalues of [Formula: see text] and [Formula: see text]. Our result identifies the fluctuation of the spatial derivative of the approximate Gaussian field in the recent paper by Dumitru and Paquette. Unlike in a similar result for Wigner matrices, for sample covariance matrices, the fluctuation may entirely vanish.

Universality of local eigenvalue statistics for some sample covariance matrices

2005 ◽  
Vol 58 (10) ◽  
pp. 1316-1357 ◽  
Author(s):  
Gérard Ben Arous ◽  
Sandrine Péché
Keyword(s):  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Eigenvalue Statistics

scholarly journals CLT for linear spectral statistics of large dimensional sample covariance matrices with dependent data

2021 ◽  
Author(s):  
Tingting Zou ◽  
Shurong Zheng ◽  
Zhidong Bai ◽  
Jianfeng Yao ◽  
Hongtu Zhu
Keyword(s):  
Covariance Matrices ◽  
Dependent Data ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Spectral Statistics

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

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.

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