Abstract: For the problem of est imating parameters, under quadratic loss and matrix loss, in a linear model with mixed coefficients, it has been given that there exist the necessary and sufficient condit ions of the uniformly minimum risk unbias (UMRU) estimators and the uniformly minimum risk equivariant( UMRE) estimators of regression coeff icients under an affine group of transformations, and the necessary and sufficient condit ions of the UMRE estimators under a transitive group of transformations respect ively.Admissibility is derived for the general least square ( GLS) estimators of regression coefficients.

Key words: mixed coeff icients, admissibility, uniformly minimum risk equivariant estimator, uniformly minimum risk unbias estimator