scholarly journals CLT for linear spectral statistics of normalized sample covariance matrices with the dimension much larger than the sample size

Bernoulli ◽  
2015 ◽  
Vol 21 (2) ◽  
pp. 1089-1133 ◽  
Author(s):  
Binbin Chen ◽  
Guangming Pan
Keyword(s):  
Sample Size ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Spectral Statistics

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.

Testing covariance structure of large-dimensional data based on Wald’s score test

2017 ◽  
Vol 06 (03) ◽  
pp. 1750009 ◽  
Author(s):  
Dandan Jiang ◽  
Qibin Zhang ◽  
Yongchang Hui
Keyword(s):  
Population Distribution ◽  
Score Test ◽  
Covariance Structure ◽  
Covariance Matrices ◽  
Sample Covariance Matrices ◽  
Sample Covariance ◽  
Nominal Size ◽  
Spectral Statistics ◽  
Non Gaussian ◽  
Rao's Score Test

This paper considers testing the covariance matrices structure based on Wald’s score test in large-dimensional setting. The tests for identity and sphericity of large-dimensional covariance matrices are reviewed by the generalized CLT for the linear spectral statistics of large-dimensional sample covariance matrices from [D. D. Jiang, Tests for large-dimensional covariance structure based on Rao’s score test, J. Multivariate Anal. 152 (2016) 28–39]. The proposed test can be applicable for large-dimensional non-Gaussian variables in a wider range. Furthermore, the simulation study is conducted to compare the proposed test with other large-dimensional covariance matrix tests. As seen from the simulation results, our proposed test is feasible for large-dimensional data without restriction of population distribution and provides the accurate and steady empirical sizes, which are almost around the nominal size.

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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