An information criterion for normal regression estimation

A discrimination information approach for evaluating the performance of a special class of linear transforms of the least squares (LS) estimates is proposed. An information criterion is defined which is shown to be a well-behaved function of the transformation matrix. The proposed criterion is related to the predictive mean squared error (PMSE) of the linear transform estimates. The relation between the information criterion and the PMSE leads to a weak necessary condition for the uniform PMSE dominance of the linear transform estimates over the LS estimates. Application of the proposed information criterion as a diagnostic for ridge regression is discussed. An illustrative example is also analyzed.