The Annals of Statistics

Characterizations of Estimability in the General Linear Model

I. S. Alalouf and G. P. H. Styan

Full-text: Open access

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.

Article information

Source
Ann. Statist., Volume 7, Number 1 (1979), 194-200.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176344564

Digital Object Identifier
doi:10.1214/aos/1176344564

Mathematical Reviews number (MathSciNet)
MR515693

Zentralblatt MATH identifier
0398.62053

JSTOR
links.jstor.org

Subjects
Primary: 62F10: Point estimation
Secondary: 15A03: Vector spaces, linear dependence, rank 15A09: Matrix inversion, generalized inverses

Keywords
Rank equalities rank additivity generalized inverses Schur complements partitioned matrices

Citation

Alalouf, I. S.; Styan, G. P. H. Characterizations of Estimability in the General Linear Model. Ann. Statist. 7 (1979), no. 1, 194--200. doi:10.1214/aos/1176344564. https://projecteuclid.org/euclid.aos/1176344564


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