Exact Linear Restrictions on Parameters in the General Linear Model with a Singular Covariance Matrix
Rudolf G. Kreijger, Heinz Neudecker · Journal of the American Statistical Association · 1977
An attempt is made to develop a best linear unbiased estimator of β in the model y = Xβ + u, with known singular covariance matrix V of u and restrictions on β. Two operational criteria for optimality are considered: minimum expected quadratic loss and minimum generalized variance. It is shown that these criteria lead to the same estimator, the well-known least-squares estimator, as developed by Theil (1971).