Linear sufficiency in a general growth curve model

The notion of linear sufficiency for the whole set of estimable functions in the general Gauss–Markov model is extended to the estimation of any special set of estimable functions in a general growth curve model. Some general results with respect to the concept of linear sufficiency are obtained, from which a necessary and sufficient condition is established for a linear transformation, {F1,F2}, of the observation matrix Y to have the property that there exists a linear function of which is the BLUE of the estimable functions .