On the best linear unbiased estimator and the linear sufficiency of a general growth curve model

Growth curve models are used to analyze repeated measures data (longitudinal data), which are functions of time. In this paper, some necessary and sufficient conditions for linear function B1YB2 to be the best linear unbiased estimator (BLUE  ) of estimable functions X1ΘX2X1ΘX2 (or K1ΘK2)K1ΘK2) under the general growth curve model were established. In addition, the representations of BLUE(K1ΘK2)BLUE(K1ΘK2) (or BLUE(X1ΘX2)BLUE(X1ΘX2)) were derived when the conditions are satisfied. Two special notions of linear sufficiency with respect to the general growth curve model are given in the end. The findings of this paper enrich some known results in the literature.