scholarly journals Spiked Eigenvalues of High-Dimensional Separable Sample Covariance Matrices

2019 ◽  
Author(s):  
Bo Zhang ◽  
Jiti Gao ◽  
Guangming Pan ◽  
Yanrong Yang
Keyword(s):  
Covariance Matrices ◽  
High Dimensional ◽  
Sample Covariance Matrices ◽  
Sample Covariance

scholarly journals Limit Properties of the Largest Entries of High-Dimensional Sample Covariance and Correlation Matrices

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Xue Ding
Keyword(s):  
Sample Size ◽  
Covariance Matrices ◽  
High Dimensional ◽  
Extreme Statistics ◽  
Correlation Matrices ◽  
Underlying Distribution ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Sample Correlation

In this paper, we consider the limit properties of the largest entries of sample covariance matrices and the sample correlation matrices. In order to make the statistics based on the largest entries of the sample covariance matrices and the sample correlation matrices more applicable in high-dimensional tests, the identically distributed assumption of population is removed. Under some moment’s assumption of the underlying distribution, we obtain that the almost surely limit and asymptotical distribution of the extreme statistics as both the dimension p and sample size n tend to infinity.

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