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

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.

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