A New Convex Estimator for Linear Regression Model

Abstract

In this article, we propose for a linear regression model a new biased estimator aimed at mitigating the impact of multicollinearity on the estimation of unknown parameters. The idea of the proposed estimator is constructed as a combination of the unbiased ridge estimator (URR) and the ordinary ridge regression estimator (ORR). The statistical properties for the new estimator and other existing estimators are found. We demonstrate the advantages of this new estimator using the mean squared error criterion, showing that its mean squared error does not exceed that of either the URR or ORR individually. This simulation study supports these theoretical results, revealing that the new estimator outperforms both the URR and ORR. This suggests that combining two estimators linearly can leverage the strengths of both, resulting in a superior estimator. To further validate the new approach, we also present a numerical example.