Limit Theorems for the Eigenvalues of Empirical Covariance Matrices

1995 ◽  
pp. 122-170
Author(s):  
Vyacheslav L. Girko
Keyword(s):  
Limit Theorems ◽  
Covariance Matrices ◽  
Empirical Covariance

Limit Theorems for the Counting Function of Eigenvalues up to Edge in Covariance Matrices

2015 ◽  
Vol 65 (1) ◽  
Author(s):  
Junshan Xie
Keyword(s):  
Limit Theorem ◽  
Limit Theorems ◽  
Counting Function ◽  
Moderate Deviation ◽  
Covariance Matrices ◽  
Local Statistics ◽  
Sample Covariance Matrices ◽  
The Central Limit Theorem ◽  
Sample Covariance ◽  
Complex Sample

AbstractWe consider the number of eigenvalues which fall into an interval for the complex sample covariance matrices. The central limit theorem and a moderate deviation principle are established when the endpoint of the interval is close to the edge of the spectrum. The proofs depend on the Four Moment Theorem about the local statistics of eigenvalues up to edge, and the rigidity theorem of the eigenvalues for sample covariance matrices.

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