Preliminary test ridge regression estimators with student’s t errors and conflicting test-statistics

Abstract.

The preliminary test ridge regression estimators (P T R R E) based on the Wald (W), Likelihood Ratio (L R) and Lagrangian Multiplier (L M) tests for estimating the regression parameters has been considered in this paper. Here we consider the multiple regression model with student t error distribution. The bias and the mean square errors (M S E) of the proposed estimators are derived under both null and alternative hypothesis. By studying the M S E criterion, the regions of optimality of the estimators are determined. Under the null hypothesis, the P T R R E based on L M test has the smallest risk followed by the estimators based on L R and W tests. However, the P T R R E based on W test performs the best followed by the L R and L M based estimators when the parameter moves away from the subspace of the restrictions. The conditions of superiority of the proposed estimators for both shrinkage parameter, k and the departure parameter, Δ are provided. Some tables for the maximum and minimum guaranteed efficiency of the proposed estimators have been given, which allows us to determine the optimum level of significance corresponding to the optimum estimator. Finally, we conclude that the estimator based on Wald test dominates the other two estimators in the sense of having highest minimum guaranteed efficiency.