The equalities of estimations under a general partitioned linear model and its stochastically restricted model

Xingwei Ren

Communications in Statistics - Theory and Methods, 2016, vol. 45, issue 22, 6495-6509

Abstract: We consider a general partitioned linear model M={y,Xβ,σ2V}={y,X1β1+X2β2,σ2V}$\mathscr {M}=\lbrace \mathbf {y}, \mathbf {X\boldsymbol{\beta }}, \sigma ^{2}\mathbf {V} \rbrace =\lbrace \mathbf {y}, \mathbf {X}_{1}\boldsymbol{\beta }_{1}+\mathbf {X}_{2}\boldsymbol{\beta }_{2}, \sigma ^{2}\mathbf {V} \rbrace$ and its stochastically restricted model without any rank assumptions. We give necessary and sufficient conditions for the equalities of the ordinary least-squares estimators (OLSEs) and the best linear unbiased estimators (BLUEs) of X1β1$\mathbf {X}_{1}\boldsymbol{\beta }_{1}$ and the equalities of the OLSEs and BLUEs of Xβ$\mathbf {X}\boldsymbol{\beta }$ under a general partitioned linear model and its stochastically restricted model. Also, we give an example for the equality of the BLUEs of Xβ$\mathbf {X}\boldsymbol{\beta }$ under a general linear model and its stochastically restricted model.

Date: 2016
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DOI: 10.1080/03610926.2014.960587

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