Necessary and sufficient conditions for a linear estimator to be admissible among linear estimators are described. The model assumed is general, allowing for relations between elements of the mean vector and covariance matrix, and allowing the covariance matrix to vary in an arbitrary subset of nonnegative definite symmetric matrices.
Lynn Roy LaMotte. "Admissibility in Linear Estimation." Ann. Statist. 10 (1) 245 - 255, March, 1982. https://doi.org/10.1214/aos/1176345707