On preliminary test almost unbiased two-parameter estimator in linear regression model with student's t errors

ABSTRACT

In this paper, the preliminary test approach to the estimation of the linear regression model with student's t errors is considered. The preliminary test almost unbiased two-parameter estimator is proposed, when it is suspected that the regression parameter may be restricted to a constraint. The quadratic biases and quadratic risks of the proposed estimators are derived and compared under both null and alternative hypotheses. The conditions of superiority of the proposed estimators for departure parameter and biasing parameters k and d are derived, respectively. Furthermore, a real data example and a Monte Carlo simulation study are provided to illustrate some of the theoretical results.

KEYWORDS:

• Almost unbiased estimator
• dominance
• preliminary test estimator
• quadratic risk

MATHEMATICS SUBJECT:

• 62J05
• 62F03

Acknowledgments

The author wishes to thank the referees and the Editor for helpful suggestions and comments which helped to improve the quality of the presentation. This work was supported by the National Science Foundation of China (Grant No. 11501254), the Natural Science Foundation of Jiangsu Province of China (Grant No. BK20140521), the Jiangsu University youth backbone teacher training project, and the Jiangsu overseas visiting scholar program for university prominent young & middle-aged teachers and presidents.