Efficiency properties of estimators in linear regression model

Abstract

A linear regression model is a statistical method employed to evaluate the strength and direction of the association between a dependent variable and one or more independent variables. Multicollinearity and measurement error are common challenges in regression modelling. These issues often reduce the reliability of regression models. To mitigate these challenges, the current study introduces novel biased estimators designed for linear regression models in the presence of multicollinearity and measurement error. The new estimators proposed in this study aim to tackle both issues simultaneously. To evaluate the efficiency of the proposed estimators, a comparison is made with existing estimators using the Mean Squared Error (MSE) matrix criterion. Theoretical results are further validated through a Monte Carlo simulation study, which allows for the examination of estimator behavior across various sample sizes, levels of multicollinearity, and degrees of measurement error. Finally, the practical applicability of the proposed estimators is demonstrated through real-life examples. newline