A note on the properties of Stein-rule and inequality restricted estimators when the regression model is over-fitted

This paper considers the effect of an erroneous inclusion of regressors on the risk properties of the Stein-rule, positive-part Stein-rule and inequality restricted and pre-test estimators in a linear regression model. The two Stein-rule estimators are considered when extraneous information is available in the form of a set of multiple equality constraints on the coefficients, while the inequality estimators are considered under the case of a single inequality constraint. It is shown that the inclusion of wrong regressors has only minimal effect on the properties of the Stein-rule and positive-part Stein-rule estimators, and no effect at all on the inequality restricted and pre-test estimators when there is a single inequality constraint.