scholarly journals A note on the largest eigenvalue of a large dimensional sample covariance matrix

1988 ◽  
Vol 26 (2) ◽  
pp. 166-168 ◽  
Author(s):  
Z.D Bai ◽  
Jack W Silverstein ◽  
Y.Q Yin
Keyword(s):  
Covariance Matrix ◽  
Sample Covariance Matrix ◽  
Largest Eigenvalue ◽  
Sample Covariance ◽  
The Largest Eigenvalue

Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by VARMA

2020 ◽  
pp. 2150022
Author(s):  
Boping Tian ◽  
Yangchun Zhang ◽  
Wang Zhou
Keyword(s):  
Covariance Matrix ◽  
Moving Average ◽  
Sample Covariance Matrix ◽  
Autoregressive Moving Average ◽  
Average Model ◽  
Largest Eigenvalue ◽  
Vector Autoregressive ◽  
Autoregressive Moving Average Model ◽  
Sample Covariance ◽  
Moving Average Model

In this paper, we derive the Tracy–Widom law for the largest eigenvalue of sample covariance matrix generated by the vector autoregressive moving average model when the dimension is comparable to the sample size. This result is applied to make inference on the vector autoregressive moving average model. Simulations are conducted to demonstrate the finite sample performance of our inference.

Analysis of grid operation state based on improved maximum eigenvalue sample covariance matrix algorithm

2021 ◽  
pp. 095965182110012
Author(s):  
Dinghui Wu ◽  
Juan Zhang ◽  
Bo Wang ◽  
Tinglong Pan
Keyword(s):  
Covariance Matrix ◽  
Signal To Noise Ratio ◽  
Poor Performance ◽  
Sample Covariance Matrix ◽  
Maximum Eigenvalue ◽  
Signal To Noise ◽  
Matrix Algorithm ◽  
Sample Covariance ◽  
Noise Ratio ◽  
Application Fields

Traditional static threshold–based state analysis methods can be applied to specific signal-to-noise ratio situations but may present poor performance in the presence of large sizes and complexity of power system. In this article, an improved maximum eigenvalue sample covariance matrix algorithm is proposed, where a Marchenko–Pastur law–based dynamic threshold is introduced by taking all the eigenvalues exceeding the supremum into account for different signal-to-noise ratio situations, to improve the calculation efficiency and widen the application fields of existing methods. The comparison analysis based on IEEE 39-Bus system shows that the proposed algorithm outperforms the existing solutions in terms of calculation speed, anti-interference ability, and universality to different signal-to-noise ratio situations.

scholarly journals Estimation of the population spectral distribution from a large dimensional sample covariance matrix

2013 ◽  
Vol 143 (11) ◽  
pp. 1887-1897 ◽  
Author(s):  
Weiming Li ◽  
Jiaqi Chen ◽  
Yingli Qin ◽  
Zhidong Bai ◽  
Jianfeng Yao
Keyword(s):  
Covariance Matrix ◽  
Spectral Distribution ◽  
Sample Covariance Matrix ◽  
Sample Covariance
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