New Robust Estimators for the Nonparametric Regression Model: Application and Simulation Study

This paper introduces new two robust kernel-based estimators (S Kernel and MM Kernel) for the nonparametric regression mode in the presence of outliers. Through comprehensive simulations, we evaluate their performance using Mean Squared Error (MSE), Mean Absolute Error (MAE), and Relative Efficiency (RE) under varying sample sizes and outlier contamination levels. Results demonstrate that robust estimators consistently outperform traditional kernel estimator, delivering the lowest estimation errors and highest efficiency, particularly in high-contamination scenarios. In contrast, the traditional kernel estimator proves highly sensitive to outliers. Also, our results highlight the superiority of the robust M Kernel estimator. This paper advances the field of robust nonparametric regression, offering practical solutions for datasets prone to outliers.