COMBINING THE LIU ESTIMATOR AND THE PRINCIPAL COMPONENT REGRESSION ESTIMATOR

Abstract

In this paper we introduce a class of estimators which includes the ordinary least squares (OLS), the principal components regression (PCR) and the Liu estimator [1]. In particular, we show that our new estimator is superior, in the scalar mean-squared error (mse) sense, to the Liu estimator, to the OLS estimator and to the PCR estimator.

Keywords:

• Liu estimator
• Mean square errror
• Multicollinearity
• r-d class estimator
• Ridge regression

ACKNOWLEDGMENTS

The authors wish to thank the editor and referee for helpful suggestions which improved an earlier version of this paper.