A comparative study of some robust nonlinear regression methods
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robust estimator, nonlinear model, outliers, M-estimator, MM-estimator.
Abstract
Least squares (LS) with Gauss-Newton method is the most widely used approach to estimate the parameters of nonlinear regression models. In the presence of outliers, even one single unusual value may have a large effect on the parameter estimates. This paper aims to introduce some popular robust nonlinear techniques that commonly used as a better alternative method to the classical least squares. This includes M-estimator and MM. In addition, the target is to compare their practical performance under a variety of circumstances such as sample size, percentage of outliers and model formula. Results of Monte Carlo simulations and real data example using R software, indicated that the best performance has been achieved by MM followed by M estimator for all possible percentages of outliers (10%, 20%, 30%, 40%) as well as all sample sizes (n=50, n=100, and n=150). Moreover, results approved that the LS estimator remains the best when there is no outlier in data.
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