A Comparative Monte Carlo Study of Hybrid and Single Robust Estimators for Nonlinear Regression Under Heavy-Tailed Error Distributions
DOI:
https://doi.org/10.62054/ijdm/0302.08Abstract
This paper presents a Monte Carlo simulation study comparing six competing robust estimation procedures: the M-estimator (M), MM-estimator (MM), Adaptive Huber estimator (AH), L1 regularization (L1), and two newly proposed hybrid methods comprising M-estimation with Adaptive Huber Loss (MAH) and MM-estimation with L1 Regularization (MM-L1) within polynomial and exponential nonlinear regression frameworks. The simulation spans three nonnormal error distributions (Uniform, Cauchy, and Exponential), two outlier contamination levels (5% and 50%) and three sample sizes (n = 50, 500, and 1,000), yielding 36 distinct experimental scenarios each evaluated over 1,000 Monte Carlo replications. Performance is assessed through Mean Squared Error (MSE). Results reveal a clear and consistent hierarchy: under mild contamination at small to moderate sample sizes, MAH consistently achieves the lowest MSE and under severe contamination at all sample sizes, or under heavy-tailed Cauchy errors, MM-L1 dominates through its complementary combination of a 50% breakdown point and L1 sparsity induction. L1 regularization alone performs weakest among the six methods under nonnormal conditions, reflecting its vulnerability arising from the squared-error data fit term. Single-method estimators M and MM occupy a middle performance tier, confirming that hybridisation systematically improves upon their individual capabilities. These findings are synthesized into a practical selection framework for researchers working with contaminated or heavy-tailed nonlinear data.
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