LMS-based robust estimation for mixed additive and multiplicative random error model

The robust estimation method with a high breakdown point for the mixed additive and multiplicative random error model (MAMREM) remains unexplored. This study therefore investigates the feasibility of applying least median of squares (LMS) estimation, a method effective for handling high proportions outliers in additive error models, to MAMREM. By integrating LMS estimation with the bias-corrected weighted least squares (bcWLS) method specific to MAMREM and addressing the computational inefficiency inherent in LMS estimation through resampling algorithms, we develop a bcWLS-LMS estimation algorithm tailored for MAMREM. Simulation experiments demonstrate that the resampling enhanced bcWLS-LMS estimation achieves significantly improved computational efficiency while maintaining robustness comparable to conventional LMS estimation. Notably, the proposed method delivers reliable parameter estimations even under extreme contamination scenarios with outliers proportion reaching 45% in MAMREM.