Estimation in singular linear models with stepwise inclusion of linear restrictions

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• 作者：Xingwei Ren ^{renxingwei123456@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62H12 ; 62J05
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：June 2016
• 年：2016
• 卷：148
• 期：Complete
• 页码：60-72
• 全文大小：411 K

文摘

In this paper, we consider the general linear model $ℳ=\{y,X\beta ,\Sigma \}$, without any rank assumptions to the model matrix $X$ and covariance matrix $\Sigma$, and its two restricted models ${ℳ}_{r_1}=\{y,X\beta |A_1\beta =r_1,\Sigma \}$ and ${ℳ}_{r_{12}}=\{y,X\beta |A\beta =r,\Sigma \}$, where 590f77">$r={(r_1^{\prime },r_2^{\prime })}^{\prime }$ and $A={(A_1^{\prime },A_2^{\prime })}^{\prime }$. We give the necessary and sufficient conditions for the BLUEs to equal under ℳ$ℳ$ and ℳ_r1${ℳ}_{r_1}$, as well as under ℳ_r1${ℳ}_{r_1}$ and ℳ_r12${ℳ}_{r_{12}}$. We also derive that the BLUEs under ℳ_r1${ℳ}_{r_1}$ are superior to the BLUEs under ℳ$ℳ$, and that the BLUEs under ℳ_r12${ℳ}_{r_{12}}$ are superior to the BLUEs under ℳ_r1${ℳ}_{r_1}$ in the sense of the covariance matrix.