scholarly journals Convergence of eigenvector empirical spectral distribution of sample covariance matrices

2020 ◽  
Vol 48 (2) ◽  
pp. 953-982 ◽  
Author(s):  
Haokai Xi ◽  
Fan Yang ◽  
Jun Yin
Keyword(s):  
Spectral Distribution ◽  
Covariance Matrices ◽  
Empirical Spectral Distribution ◽  
Sample Covariance Matrices ◽  
Sample Covariance

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.

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