Preliminary test Liu estimators based on the conflicting W,LR and LM tests in a regression model with multivariate Student-<Emphasis Type="Italic">t</Emphasis> error

In this paper, the problem of estimation of the regression coefficients in a multiple regression model with multivariate Student-t error is considered under the multicollinearity situation when it is suspected that the regression coefficients may be restricted to a linear manifold. The preliminary test Liu estimators (PTLE) based on the Wald, Likelihood ratio (LR) and Lagrangian multiplier (LM) tests are given. The bias and mean square error (MSE) of the proposed estimators are derived and conditions of superiority of these estimators are provided. In particular, we show that in the neighborhood of the null hypothesis, the PTLE based on the LM test has the best performance followed by the estimators based on LR and W tests, while the situation is reversed when the parameter moves away from the manifold of the restriction. Furthermore, the optimum choice of the level of significance is also discussed.