Preliminary test almost unbiased two-parameter estimators with student’s t errors and conflicting test statistics

Abstract

In this paper, we consider the preliminary test approach to the estimation of the regression parameter in a multiple regression model under multicollinearity situation. The preliminary test almost unbiased two-parameter estimators based on the Wald, the Likelihood ratio, and the 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 errors. The bias and quadratic risk of the proposed estimators are derived and compared. Furthermore, a Monte Carlo simulation is provided to illustrate some of the theoretical results.

Keywords:

• Almost unbiased estimator
• preliminary test estimator
• quadratic risk
• student’s t error

Mathematics Subject Classification:

• 62J07
• 62F03

Acknowledgments

We would like to thank the referees and the editor for helpful suggestions and comments which helped to improve the quality of the presentation.

Additional information

Funding

This work was supported by the National Science Foundation of China (Grant No. 11501254), the Jiangsu University youth backbone teacher training project, and the Jiangsu overseas visiting scholar program for university prominent young & middle-aged teachers and presidents.