(a) Using (5.12) and (5.13), verify that \(\Omega^{*} \Omega^{*-1}=I\) and \(\Omega^{*-1 / 2} \Omega^{*-1 / 2}=\) \(\Omega^{*-1}\).

(b) Show that \(y^{* *}=\sigma_{\epsilon} \Omega^{*-1 / 2} y^{*}\) has a typical element given by (5.14).

(c) Show that for \(ho=0\), (5.14) reduces to \(\left(y_{i t}-\theta \bar{y}_{i \text {. }}ight)\).

(d) Show that for \(\sigma_{\mu}^{2}=0\), (5.14) reduces to \(y_{i t}^{*}\).

Transcribed Image Text:

22* = o(INJ) + 0 (INE) (5.12)