Positive-rule stein-type almost unbiased ridge estimator in linear regression model

Abstract

In this article, when it is suspected that regression coefficients may be restricted to a subspace, we discuss the parameter estimation of regression coefficients in a multiple regression model. Then, in order to improve the preliminary test almost ridge estimator, we study the positive-rule Stein-type almost unbiased ridge estimator based on the positive-rule stein-type shrinkage estimator and almost unbiased ridge estimator. After that, quadratic bias and quadratic risk values of the new estimator are derived and compared with some relative estimators. And we also discuss the option of parameter k. Finally, we perform a real data example and a Monte Carlo study to illustrate theoretical results.

Keywords:

• Positive-rule Stein-type almost unbiased ridge estimator
• Almost unbiased ridge estimator
• Preliminary test almost ridge estimator
• Quadratic bias
• quadratic risk.

Mathematics Subject Classification:

• 62F03
• 62F30
• 62J05

Acknowledgments

The author is very grateful to the editor and the two anonymous referees for their positive and constructive comments and suggestions which help us to improve the quality and presentation of this article.

Funding

This work is supported by the Fundamental Research Funds for the Central Universities, project No. CQDXWL-2013-007.