An almost unbiased Liu-type estimator in the linear regression model

Abstract

A biased estimator, compared to least squares estimators, is one of the most used statistical procedures to overcome the problem of multicollinearity. Liu-type estimators, which are biased estimators, are preferred in a wide range of fields. In this article, we propose an almost unbiased Liu-type (AUNL) estimator and discuss its performance under the mean square error matrix criterion among existing estimators. The proposed AUNL estimator is a general estimator and is based on the function of a single biasing parameter. It includes an ordinary least squares estimator, an almost unbiased ridge estimator, an almost unbiased Liu estimator, and an almost unbiased two-parameter estimator. Finally, real data examples and a Monte Carlo simulation are provided to illustrate the theoretical results.