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

• Published in: Linear algebra and its applications Vol. 321; no. 1; pp. 387 - 398
• Main Authors: Zhang, Bao-Xue, Zhu, Xian-Hai
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.12.2000
• Subjects: Gauss–Markov estimator; Generalized least-squares estimator; Growth curve model; Ordinary least-squares estimator; Weighted least-squares estimation; 62J05; Gauss–Markov estimator; Generalized least-squares estimator; Growth curve model; Weighted least-squares estimation; Ordinary least-squares estimator
• ISSN: 0024-3795; 1873-1856
• DOI: 10.1016/S0024-3795(00)00197-X

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.