We present a shrinkage estimator for the EEG spatial covariance matrix of the background activity. We show that such an estimator has some advantages over the maximum likelihood and sample covariance estimators when the number of available data to carry out the estimation is low. We find sufficient conditions for the consistency of the shrinkage estimators and results concerning their numerical stability. We compare several shrinkage schemes and show how to improve the estimator by incorporating known structure of the covariance matrix.
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