Performance of Preliminary Test Estimators for Error Variance Based on W, LR and LM Tests

The performances of preliminary test estimators for error variance based on W, LR and LM tests in a normal linear model are considered in this paper. Firstly, the risks of the proposed estimators are derived and compared by theoretical analysis and numerical calculation, respectively. The results show that their risks are related to the equality constraint error and the critical value of test. Moreover, the minimum value of the risks can be achieved when the critical value of test equals to one. Secondly, the superiority conditions of the proposed estimators are discussed. Finally, the results are illustrated by a simulation example.