SIMULTANEOUS ESTIMATION IN A RESTRICTED LINEAR-MODEL

We consider a linear normal model Y = X theta + e with theta verifying a linear restriction and the standard estimators <(theta)over cap> (u nrestricted MLE) and theta (restricted MLE). We prove that theta* is preferable to <(theta)over cap> using a new and strong criterion which implies the domination under other usual criteria; in particular it i s proven that the standard simultaneous confidence intervals centered at theta have more confidence than those centered at <(theta)over cap >. (C) 1997 Academic Press.