Fuller and Battese (1973) transformation for the one-way random effects model.

(a) Verify (2.17) and check that \(\Omega^{-1} \Omega=I\) using (2.18).

(b) Verify that \(\Omega^{-1 / 2} \Omega^{-1 / 2}=\Omega^{-1}\) using (2.20) and (2.19).

(c) Premultiply \(y\) by \(\sigma_{u} \Omega^{-1 / 2}\) from (2.20), and show that the typical element is \(y_{i t}-\theta \bar{y}_{i}\). where \(\theta=1-\left(\sigma_{v} / \sigma_{1}ight)\).

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= E(uu) = ZE ()Z +E(vv) = o(INJT) + o(IN & IT) (2.17)