A study on the performance of five robust nonlinear regression estimators
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robust estimator, nonlinear model, outliers, simulation.
Abstract
Nonlinear regression is one of the most popular and widely used models in analysing the effect of explanatory variables on a response variable when the underling regression function is nonlinear. It has many applications in scientific research such as dose response studies conducted in agricultural sciences, toxicology and other biological sciences. Estimating the parameters of a nonlinear regression model is usually carried out by the least squares (LS. However, In the presence of outliers, even one single unusual value may have a large effect on the parameter estimates. The aim of this paper is to introduce the most commonly used methods as a better choice to the classical least squares. This includes M-estimator, MM-estimator, CM-estimator, tau-estimator and mtl-estimator. Moreover, 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 using R software, indicated that the best performance has been achieved by MM followed by CM 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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