General admissibility for linear estimators of multivariate random regression coefficients and parameters with respect to a restricted parameter set

This paper considers the linear model effected by random disturbance, Y = XB + ɛ, where $ \left \begin{gathered} B \hfill \\ \varepsilon \hfill \\ \end{gathered} \right] \sim \left( {\left \begin{gathered} A\Theta \hfill \\ 0 \hfill \\ \end{gathered} \right],V \otimes \Sigma } \right) $ \left \begin{gathered} B \hfill \\ \varepsilon \hfill \\ \end{gathered} \right] \sim \left( {\left \begin{gathered} A\Theta \hfill \\ 0 \hfill \\ \end{gathered} \right],V \otimes \Sigma } \right) , and Θ ^T A ^T X ^T NXAΘ ⩽ Σ. It gives a definition for general admissible estimator of a linear function SΘ + GB of random regression coefficients and parameters. The necessary and sufficient conditions for LY and LY + C to be general admissible estimators of SΘ + GB in the class of both homogenous and non-homogenous linear estimators are obtained. The conclusion is not dependent of whether or not SΘ +GB is estimable.