Optimal estimators in misspecified linear regression model with an application to real-world data

TL;DR

This paper introduces new estimators for linear regression models with multicollinearity and misspecification, demonstrating their advantages through theoretical conditions, simulations, and real data applications.

Contribution

It proposes the Sample Information Optimal Estimator (SIOE) and Stochastic Restricted Optimal Estimator (SROE) for improved estimation under model misspecification and multicollinearity.

Findings

Proposed estimators outperform existing ones in MSEM criteria.

Theoretical superiority conditions are derived.

Simulation and real data examples validate the estimators' effectiveness.

Abstract

In this article, we propose the Sample Information Optimal Estimator (SIOE) and the Stochastic Restricted Optimal Estimator (SROE) for misspecified linear regression model when multicollinearity exists among explanatory variables. Further, we obtain the superiority conditions of proposed estimators over some other existing estimators in the Mean Square Error Matrix (MSEM) criterion in a standard form which can apply to all estimators considered in this study. Finally, a real world example and a Monte Carlo simulation study are presented for the proposed estimators to illustrate the theoretical results.