Estimability in Partitioned Linear Models
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 $E(Y) = X_0\pi_0 + X_2\pi_2$.
Permanent link to this document: http://projecteuclid.org/euclid.aos/1176344960
Digital Object Identifier: doi:10.1214/aos/1176344960
Mathematical Reviews number (MathSciNet): MR560736
Zentralblatt MATH identifier: 0432.62049