The shrinkage preliminary test estimator (SPTE) base on the Wald (W), Likelihood Ratio (LR), Lagrangian Multiplier (LM) tests are given. Their bias, mean square error (MSE), and risk functions are derived and compared. In the neighborhood of the null hypothesis the SPTE based on the LM test has the smallest risk followed by the LR based estimators and the estimator based on the W test is the worst. However, the SPTE based on the W test performs the best followed by the LR based estimator when the parameter moves away from the subspace of the restriction and the LM based estimator is the worst. It has been shown that the optimum choice of the level of significance becomes the choice by using the W and SPTE which is unusual in traditional PTE.