Using a technique originated by A. Olsen, J. Seely, and D. Birkes (Ann. Statist. 4 (1976), 878-890) and developed by L. R. LaMotte (Ann. Statist. 10 (1982), 245-256) we establish necessary conditions of C. R. Rao's type (Ann. Statist. 4 (1976), 1023-1037) for a linear estimator to be admissible among the class of linear estimators in a general linear model. They are shown to be sufficient for the regression model with a nonnegative definite covariance matrix and for the model with the mean lying in a subspace and the covariance operators varying through the set of all nonnegative definite symmetric matrices. From these results necessary and/or sufficient conditions for admissibility of nonhomogeneous estimators are also derived.
