This paper consider the estimation of population mean of a multivariate normal population with unknown covariance matrix. We consider three shrinkage preliminary test (SPT) maximum likelihood estimators (SPTMLE) based on the Wald (W), Likelihood Ratio (LR) and Lagrangian Multiplier (LM) tests for estimating mean. Using a specific quadratic loss function, the conditions of superiority of the proposed estimators for departure parameter are derived. Some tables for maximum and minimum guaranteed relative efficiency of the proposed estimators have been provided. These tables allow us to determine the optimum level of significance corresponding to the optimum estimator among proposed estimators. It has been shown by computationally that the SPTMLE based on W test dominates estimators based on LM and LR tests in the sense of having highest minimum guaranteed efficiency.