Abstract:
Maximum-likelihood estimation of the variance of the disturbances in a linear regression is
considered in the context of exact linear restrictions on the coefficient vector. The exact risk
function for the associated preliminary-test estimator of this variance is derived and evaluated
numerically on the basis of relative quadratic loss. Our results indicate that in practical situations
the risk of the pre-test estimator differs only slightly from that of the naive estimator which
ignores the restrictions without testing. Applying the coefficient restrictions without testing their
validity is not recommended.
