Simultaneous Estimation in a Restricted Linear Model,

We consider a linear normal modelY=X[theta]+ewith[theta]verifying a linear restriction and the standard estimators [theta](unrestricted MLE) and[theta]* (restricted MLE). We prove that[theta]* is preferable to [theta]using a new and strong criterion which implies the domination under other usual criteria; in particular it is proven that the standard simultaneous confidence intervals centered at[theta]* have more confidence than those centered at [theta].