Abstract: In this paper, we proposed the preliminary test two-parameter estimators based on the Wald (W), the Likelihood Ration (LR) and the Lagrangian Multiplier (LM) tests, when it is suspected that the regression parameter may be restricted to a subspace. The bias and the mean square error (MSE) of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained.