A NEW ROBUST METHOD OF DEALING WITH MULTICOLLINEARITY AND OUTLIERS IN REGRESSION ANALYSIS: SIMULATIONS AND APPLICATIONS

Abstract

Ordinary Least Squares (OLS) regression is known to be unreliable in the presence of outliers and multicollinearity, leading to biased parameter estimates, inflated standard errors, and reduced predictive accuracy. Limited studies have considered estimators that can co-handle the two problems (multicollinearity and outliers). However, to explore further methods, this study proposes the Robust M-version of the New Biased Based Estimator (M-NBB), designed to handle both multicollinearity and outliers effectively. Theoretical properties of the proposed estimator were established under fundamental conditions and validated through Monte Carlo simulations implemented in R-statistical programming. The simulation study involved 1,000 replications across eight sample sizes and three explanatory variables exhibiting varying degrees of multicollinearity. Additionally, 10% and 20% of the generated observations were contaminated with outliers of various magnitudes under error variances. The performance of the estimators was evaluated using the Mean Squared Error (MSE). The simulation results revealed that the proposed estimator outperformed existing estimators across all conditions. To further validate its effectiveness, the estimator was applied to real-life data. The findings suggest that the M-NBB estimator is a robust and reliable alternative for practitioners dealing with datasets affected by both multicollinearity and outliers.

Keywords: Ordinary Least Squares, Multicollinearity, outliers, Monte Carlo simulation, Estimator