A New Robust LQS-NTP Estimator for Mitigating Correlated Endogenous Variables and Extreme Observations in Linear Regression Models: Theoretical Development and Applications

Abstract

This study proposes a Robust Least Quantile of Squares–New Two-Parameter (LQS-NTP) estimator for addressing multicollinearity and extreme observations in linear regression models. The proposed estimator combines the high-breakdown robustness of the Least Quantile of Squares (LQS) method with the shrinkage properties of the New Two-Parameter (NTP) estimator. The Mean Squared Error (MSE) of the proposed estimator was derived, and its biasing parameters were obtained by minimizing the corresponding MSE. The performance of the proposed estimator was assessed using real-life Boston Housing and Portland Cement datasets and compared with some already existing methods. The data sets exhibited substantial multicollinearity, together with several outlying observations. The proposed LQS-NTP estimator achieved the lowest MSE of both data employed. These results demonstrate that the proposed estimator provides an effective alternative for regression estimation in the simultaneous presence of multicollinearity and extreme observations.