Characterizations of Estimability in the General Linear Model
The Annals of Statistics · 1979 · Volume 7 · Issue 1
Abstract
In the general linear model $\mathscr{E}(\mathbf{y}) = \mathbf{X\beta}$, the vector $\mathbf{A\beta}$ is estimable whenever there is a matrix $\mathbf{B}$ so that $\mathscr{E}(\mathbf{By}) = \mathbf{A\beta}$. Several characterizations of estimability are presented along with short easy proofs. The characterizations involve rank equalities, generalized inverses, Schur complements and partitioned matrices.
Keywords
15A03, 15A09, 62F10, generalized inverses, partitioned matrices, rank additivity, Rank equalities, Schur complements
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