Two-Sample Covariance Matrix Testing and Support Recovery in High-Dimensional and Sparse Settings

Estimation of Population covariance matrix from samples is important in a wide range of areas of statistical analysis. In the estimation, the sample covariance matrix, which is the most natural and standard estimator, often performs badly. With the collection of large high-dimensional data in scientific investigation, the related covariance matrix becomes complicated to deal with. Therefore, for the convenience in computing and analyzing, we need to simplify the covariance matrix. This method is referred as regularization. In this paper, we will consider a proof for a construction of covariance regularization by tapering.

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A High‐Dimensional Classification Rule Using Sample Covariance Matrix Equipped With Adjusted Estimated Eigenvalues

Stat ◽

10.1002/sta4.358 ◽

2021 ◽

Author(s):

Seungchul Baek ◽

Hoyoung Park ◽

Junyong Park

Keyword(s):

Covariance Matrix ◽

Classification Rule ◽

Sample Covariance Matrix ◽

High Dimensional ◽

Dimensional Classification ◽

Sample Covariance

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Asymptotic Distributions of Functions of the Eigenvalues of the Sample Covariance Matrix and Canonical Correlation Matrix in Multivariate Time Series

10.21236/ada170282 ◽

1986 ◽

Author(s):

M. Taniguchi ◽

P. R. Krishnaiah

Keyword(s):

Time Series ◽

Covariance Matrix ◽

Canonical Correlation ◽

Correlation Matrix ◽

Multivariate Time Series ◽

Asymptotic Distributions ◽

Sample Covariance Matrix ◽

Sample Covariance

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

Proceedings of the Institution of Mechanical Engineers Part I Journal of Systems and Control Engineering ◽

10.1177/09596518211001270 ◽

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.

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