  We tackle covariance estimation in low-sample scenarios, employing a
structured covariance matrix with shrinkage methods. These involve convexly
combining a low-bias/high-variance empirical estimate with a biased
regularization estimator, striking a bias-variance trade-off. Literature
provides optimal settings of the regularization amount through risk
minimization between the true covariance and its shrunk counterpart. Such
estimators were derived for zero-mean statistics with i.i.d. diagonal
regularization matrices accounting for the average sample variance solely. We
extend these results to regularization matrices accounting for the sample
variances both for centered and non-centered samples. In the latter case, the
empirical estimate of the true mean is incorporated into our shrinkage
estimators. Introducing confidence weights into the statistics also enhance
estimator robustness against outliers. We compare our estimators to other
shrinkage methods both on numerical simulations and on real data to solve a
detection problem in astronomy.
