Weaker MSE Criteria and Tests for Linear Restrictions in Regression Models with Nonspherical Disturbances

Abstract

This paper extends, in an asymptotic sense, the strong and the weaker mean square error criteria and corresponding tests to linear models with non-spherical disturbances where the error covariance matrix is unknown but a consistent estimator for it is available. The mean square error tests of Toro-Vizcorrondo and Wallace (1968) and Wallace (1972) test for the superiority of restricted over unrestricted linear estimators in a least squares context. This generalization of these tests makes them available for use with GLS, Zellner’s SUR, ZSLS, 3SLS, tests of over identification, and so forth.