Characterizations of Estimability in the General Linear Model
I. S. Alalouf, George P. H. Styan · The Annals of Statistics · 1979
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.