Characterizations of Estimability in the General Linear Model
Alalouf, I. S. ; Styan, G. P. H.
Ann. Statist., Tome 7 (1979) no. 1, p. 194-200 / Harvested from Project Euclid
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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.
Publié le : 1979-01-14
Classification:  Rank equalities,  rank additivity,  generalized inverses,  Schur complements,  partitioned matrices,  62F10,  15A03,  15A09 
@article{1176344564,
     author = {Alalouf, I. S. and Styan, G. P. H.},
     title = {Characterizations of Estimability in the General Linear Model},
     journal = {Ann. Statist.},
     volume = {7},
     number = {1},
     year = {1979},
     pages = { 194-200},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176344564}
}

Alalouf, I. S.; Styan, G. P. H. Characterizations of Estimability in the General Linear Model. Ann. Statist., Tome 7 (1979) no. 1, pp.  194-200. http://gdmltest.u-ga.fr/item/1176344564/