Evaluation of the Predictive Performance of the Liu Estimator

Abstract

Multiple linear regression models are frequently used in predicting (forecasting) unknown values of the response variable y. In this case, a regression model ability to produce an adequate prediction equation is of prime importance. This paper discusses the predictive performance of the Liu estimator compared to ordinary least squares, as well as to two other popular biased estimators, principal components and Ridge regression estimators. The theoretical results are illustrated by a numerical example, and a region is established where the Liu estimator is uniformly superior to the other three estimators.

Keywords:

• Biased estimation
• Liu estimator
• Multicollinearity
• Prediction mean squared error.

Mathematics Subject Classification:

• Primary 62J05
• Secondary 62J07.