On the Stochastic Restricted Almost Unbiased Estimators in Linear Regression Model

Abstract

In this article, the stochastic restricted almost unbiased ridge regression estimator and stochastic restricted almost unbiased Liu estimator are proposed to overcome the well-known multicollinearity problem in linear regression model. The quadratic bias and mean square error matrix of the proposed estimators are derived and compared. Furthermore, a numerical example and a Monte Carlo simulation are given to illustrate some of the theoretical results.

Keywords:

• Liu estimator
• Multicollinearity
• Ridge estimator
• Stochastic linear restrictions
• Stochastic restricted almost unbiased Liu estimator
• Stochastic restricted almost unbiased ridge estimator

Mathematics Subject Classification:

• Primary 62J05
• 62J07

Acknowledgments

The authors are most grateful to the anonymous reviewer and the Editor for valuable comments and suggestions that helped to improve the quality of the article. This work was supported by the Fundamental Research Funds for the Central Universities of China (No. CDJXS12100016) and National Natural Science Foundation of China (no. 11171361).