New estimators in a partial linear model depending on an unbiased ridge regression estimator

¹ Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Anbar, Iraq.
² Department of Mathematics, College of Education for Pure Sciences, University of Anbar, Anbar, Iraq.

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Published online: 13 May 2026

Abstract

This paper introduces two new estimators based on the philosophy of unbiased ridge regression estimation, where the parameters are part of a partial linear model suffering from multicollinearity. These proposed estimators are called the Difference-Based Unbiased Ridge Estimator ${\widehat{\beta }}_{\mathit{DB}-\mathit{URR}}$ and the Difference-Based Modified Unbiased Ridge Estimator ${\widehat{\beta }}_{\mathit{DB}-\mathit{MUR}}$ for the regression parameters β. The Mean Squared Error Matrix (MSEM) criterion is employed to compare the proposed estimators against the Difference-Based Ordinary Least Squares estimator ${\widehat{\beta }}_{\mathit{DB}-\mathit{OLS}}$ and the Difference-Based Ordinary Ridge Estimator ${\widehat{\beta }}_{\mathit{DB}-\mathit{ORR}}$. Finally, the performance of the new estimators is evaluated through a comprehensive simulation study and a numerical example.