Comparisons of estimators for regression coefficient in a misspecified linear model with elliptically contoured errors

Abstract

In a misspecified linear regression model with elliptically contoured errors, the exact risks of generalized least squares (GLS), restricted least squares (RLS), preliminary test (PT), Stein-rule (SR) and positive-rule shrinkage (PRS) estimators of regression coefficient are derived. Risk superiority conditions dependent on prior constraint error and the model specification error are obtained. When the model is misspecified and the error terms obey the elliptically contoured distribution, it is shown analytically that the PRS estimator dominates uniformly the SR estimator. However, the PRS and SR estimators do not dominate uniformly the GLS estimator. Furthermore, the dominance of the RLS estimator over the GLS estimator does not hold necessarily even if the model has linear constraint.