## The Annals of Statistics

### Characterizations of Estimability in the General Linear Model

#### 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

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