On a criterion for extrapolation in multivariate normal regression

In a full (or less than full) rank normal multivariate regression model, the existence of an unbiased estimate of the distribution associated to any future observation vector is studied. A necessary and sufficient condition in terms of the point at which the future observation vector will be taken introduced to consider the validity of extrapolation. The results given here generalize some results of Silvey [3] and the related results of O’Reilly [1].