Performance of the preliminary test two-parameter estimators based on the conflicting test statistics in a regression model with Student's t error

Abstract

In this paper, we consider the preliminary test approach for the estimation of the regression parameter in a multiple regression model under a multicollinearity situation. The preliminary test two-parameter estimators based on the Wald (W), likelihood ratio, and Lagrangian multiplier tests are given, when it is suspected that the regression parameter may be restricted to a subspace and the regression error is distributed with multivariate Student's t distribution. The bias and mean square error of the proposed estimators are derived and compared. The conditions of superiority of the proposed estimators are obtained. Finally, we conclude that the optimum choice of the level of significance becomes the traditional choice by using the Wald test.

Keywords:

• two-parameter estimator
• multicollinearity
• preliminary test estimator
• mean square error
• Student's t error

AMS Classifications :

• 62J07
• 62F03

Acknowledgements

The authors are grateful to the anonymous referees and the Editor for their valuable comments and suggestions which helped to improve the quality of the article. This work was supported by a grant from the National Natural Science Foundation of China (No. 11001286).