On consistency, natural restrictions and estimability under classical and extended growth curve models

For the general growth curve model {Y,X1ΘX2,σ2(Σ2⊗Σ1)} with X1X1, X2X2, Σ1Σ1 and Σ2Σ2 of arbitrary ranks, we study the following three problems:(I)Necessary and sufficient conditions for the model to be consistent.(II)Natural restrictions to the parameter matrix ΘΘ.(III)Unbiasedness of linear estimators and estimability of parameter matrices.Some extensions of this work to the extended growth curve model {Y,∑i=1tX1iΘiX2i,σ2(Σ2⊗Σ1)} are also given.