Performances of the Positive-Rule Stein-Type Ridge Estimator in a Linear Regression Model with Spherically Symmetric Error Distributions

Abstract

In this article, the positive-rule Stein-type ridge estimator (PSRE) is introduced for the parameters in a multiple linear regression model with spherically symmetric error distributions when it is suspected that the parameter vector may be restricted to a linear manifold. The bias and quadratic risk functions of the PSRE are derived and compared with some related competing estimators in literatures. Particularly, some sufficient conditions are derived for superiority of the PSRE over the ordinary ridge estimator, the restricted ridge estimator and the preliminary test ridge estimator, respectively. Furthermore, some graphical results are provided to illustrate some of the theoretical results.

Keywords:

• Multivariate Student-t distribution
• Preliminary test
• Quadratic risk
• Ridge estimator
• Stein-type estimator

Mathematics Subject Classification:

• Primary 62J07
• Secondary 62F03

Acknowledgments

The authors are very grateful to the two anonymous referees for their helpful suggestions which improved the presentation of the article. This research was supported by the National Natural Science Foundation of China (No. 11001286 and No. 11201515).