Abstract
In this paper we compare the mean square error matrices of the ordinary least squares estimator, the restricted least squares estimator and a generalisation of the ordinary ridge estimator. We establish necessary and sufficient conditions for the mean square error matrix of the ordinary least squares estimator to exceed that of the ridge estimator by a positive semidefinite matrix and necessary and sufficient conditions for the mean square error matrix of the ridge estimator to exceed that of the restricted least squares estimator by a positive semi-definite matrix.
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