Admissible linear estimation in a general Gauss-Markov model with an incorrectly specified dispersion matrix

Necessary and sufficient conditions are established for the set of all admissible linear estimators under M0 to be contained in the corresponding set of estimators under M, where M0 and M are general Gauss-Markov models with identical model matrices but different dispersion matrices. As preliminary results, certain new characterizations of admissible linear estimators are derived, including explicit expressions for the general representations of such estimators and extensions of the admissibility criteria given by [10], 1023-1037) and [4], 11-30).