Adaptive Huber-LAD Hybrid Estimation for Robust Nonlinear Regression under Asymmetric Error Distributions

AbstractOrdinary Least Squares (OLS) regression performs poorly when error distributions areasymmetric, skewed, heavy-tailed, or contaminated by outliers. This study proposes a novelAdaptive Huber-LAD Hybrid (AHLH) estimator for nonlinear regression, combining theefficiency of the Huber estimator with the robustness of Least Absolute Deviation (LAD). Theproposed estimator employs a data-driven adaptive threshold based on residual skewness andkurtosis and is implemented using an Iteratively Reweighted Least Squares (IRLS) algorithm.Theoretical properties, including consistency and asymptotic normality, are established undermild regularity conditions. Monte Carlo simulation studies demonstrate that the proposedestimator consistently outperforms OLS, LAD, and fixed-threshold Huber estimators in terms ofestimation accuracy and robustness under asymmetric error distributions. A healthcare case studyfurther confirms its superior predictive performance in the presence of skewed clinical data. Theproposed AHLH estimator provides a reliable and computationally efficient alternative for robustnonlinear regression when the assumption of normal errors is violated.