Estimability in Partitioned Linear Models
Open Access
- 1 March 1980
- journal article
- Published by Institute of Mathematical Statistics in The Annals of Statistics
- Vol. 8 (2), 399-406
- https://doi.org/10.1214/aos/1176344960
Abstract
Some estimability facts for partitioned linear models with constraints are presented. For a model $E(Y) = X_1\pi_1 + X_2\pi_2$ with constraints on $\pi_1$ and $\pi_2$ a reduced model is derived that contains all information regarding the estimability (and also regarding the blues) of parametric functions $b'\pi_2$. For a model $E(Y) = X_0\pi_0 + X_1\pi_1 + X_2\pi_2$ with constraints on $\pi_0, \pi_1$ and $\pi_2$, several necessary and sufficient conditions are given for when estimability of $b'\pi_2$ in the original model is equivalent to estimability in the simpler model $E(Y) = X_0\pi_0 + X_2\pi_2$.