General optimality and general admissibility of linear estimates of the mean matrix (Q1309120)

We introduce a definition of general optimality in estimating a linear estimable function \(S_{k \times p}\Theta\) (\(S' \subset \mu(X')\)) of the mean matrix \(\Theta\) in the multivariate linear model: \[ Y_{n \times m}= X_{n \times p} \Theta+\varepsilon,\quad E(\varepsilon)=0,\quad\text{ Cov}(\vec\varepsilon)=\sigma^ 2U_{n \times n} \otimes V_{m \times m},\quad n \geq m. \] {}.