A New Mixed Biased Estimator for Ill-Conditioning Challenges in Linear Regression Model With Chemometrics Applications

Abstract

In linear regression models, the ordinary least squares (OLS) method is used to estimate the unknown regression coefficients. However, the OLS estimator may provide unreliable estimates in non-orthogonal models. This article introduces a novel mixed-biased estimator to address the challenges posed by the non-orthogonal model. The proposed estimator is derived through a combination of two estimators, namely, the Stein and ridge estimators. The theoretical properties of the proposed estimator are discussed. Moreover, we suggest estimation methods to estimate the value of the shrinkage parameters for the proposed estimator. We compare the performance of the proposed estimator with the Stein estimator, the ridge estimator with standard and two best ridge parameters and the ordinary least square estimator. This evaluation is based on the mean squared error performance criterion, using both a simulation study and two practical applications related to cement and crock datasets. The simulation study and applications results show that the proposed estimator performs better than the other considered estimators.