Gauss–Markov and weighted least-squares estimation under a general growth curve model

Abstract

Gauss–Markov estimator of X 1BX ′ 2 under a general growth curve model {Y,X 1BX ′ 2,V 2⊗V 1} is given. Necessary and sufficient conditions for equality between A 1YA ′ 2 and B 1YB ′ 2 , where A i=X i(X ′ iW iX i) +X ′ iW i , B i=X i(X ′ iS iX i) +X ′ iS i , with W i,S i being any matrix, i=1,2, are derived. Finally, a number of criteria for A 1YA ′ 2 to coincide with the Gauss–Markov estimator of X 1BX ′ 2 are established.