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

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 β̂DB- URR and the Difference-Based Modified Unbiased Ridge Estimator β̂DB- 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 β̂DB- OLS and the Difference-Based Ordinary Ridge Estimator β̂DB- ORR. Finally, the performance of the new estimators is evaluated through a comprehensive simulation study and a numerical example.