Stein-rule estimation under an extended balanced loss function

Abstract

This paper extends the balanced loss function to a more general setup. The ordinary least squares estimator (OLSE) and Stein-rule estimator (SRE) are exposed to this general loss function with quadratic loss structure in a linear regression model. Their risks are derived when the disturbances in the linear regression model are not necessarily normally distributed. The dominance of OLSE and SRE over each other and the effect of departure from normality assumption of disturbances on the risk property are studied.

Keywords:

• linear regression model
• Stein-rule estimator
• ordinary least squares estimator
• balanced loss function
• non-normal disturbances

Acknowledgements

The authors are grateful to the referee and to the associate editor for the comments that improved the exposition of the paper. The first author gratefully acknowledges the financial support from Alexander von Humboldt Foundation, Germany, in the form of the Humboldt Fellowship.