Covariance Matrix Estimation from Correlated Sub-Gaussian Samples via the Shrinkage Estimator

Covariance matrix estimation is of great importance in statistical signal processing. This paper considers covariance matrix estimation from correlated complex sub-Gaussian samples via the shrinkage estimator. We establish non-asymptotic error bounds for this estimator in both tail and expectation forms. Our theoretical results demonstrate that the error bounds depend on the signal dimension, the sample size, the shape parameter, and the shrinkage coefficient $\alpha$. These results reveal that the shrinkage estimator can reduce the sample complexity of the standard sample covariance matrix estimator when the target matrix is reliable and $\alpha$ is properly chosen.