A note on the inverse-partitioned-matrix method in linear regression analysis (Q1083809)

Let the classical regression model \(y=X\beta +\sigma \epsilon\), \(E(\epsilon)=0\), Cov \(\epsilon\) \(=V\) be given. It is shown that the inverse-partitioned-matrix method due to \textit{C. R. Rao} [Linear statistical inference and its application. 2nd ed. (1973; Zbl 0256.62002)] can easily be understood if the prediction problem for linear models is considered.