Adjustive Liu-Type Estimators in Linear Regression Models

Abstract

In this article, we aim to put forward the notion of adjustive Liu-type estimator (ALTE) in the linear regression model. First, the explicit expression of the optimal selection of the adjustive factors is derived under the PRESS criterion through matrix techniques. Then, the results are applied to the dataset on Portland cement. Moreover, to select biasing parameters from the theoretical point of view, we extend ALTE to the generalized version (GALTE) and obtained the optimal ones. The results of the Portland cement data show that ALTE's and GALTE's can substantially improve the ordinary least squares estimator and Liu-type estimators.

Keywords:

• Adjustive Liu-type estimator
• Generalized adjustive Liu-type estimator
• Liu-type estimator
• PRESS criterion

Mathematics Subject Classification:

• 62J05
• 62J07

Acknowledgments

The author is very grateful to the referee for so many valuable comments and constructive suggestions which resulted in the present version. Thanks also to Professor Xu-Qing Liu for some comments during preparation of the original version of the article. This work was partially supported by grant HXGJ09016.