Covariance Matrix Estimation from Correlated Sub-Gaussian Samples
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This paper studies the problem of estimating a covariance matrix from correlated sub-Gaussian samples. We consider using the correlated sample covariance matrix estimator to approximate the true covariance matrix. We establish non-asymptotic error bounds for this estimator in both real and complex cases. Our theoretical results show that the error bounds are determined by the signal dimension n, the sample size m and the correlation pattern B. In particular, when the correlation pattern B satisfies tr(B)=m, ||B||_F=O(m^1/2), and ||B||=O(1), these results reveal that O(n) samples are sufficient to accurately estimate the covariance matrix from correlated sub-Gaussian samples. Numerical simulations are presented to show the correctness of the theoretical results.
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