### Estimability in Partitioned Linear Models

Justus Seely and David Birkes
Source: Ann. Statist. Volume 8, Number 2 (1980), 399-406.

#### 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 $E(Y) = X_0\pi_0 + X_2\pi_2$.

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Primary Subjects: 62J99
Secondary Subjects: 62K99
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