Finite-sample comparison of robust estimators for nonlinear regression using Monte Carlo simulation: Part I. Univariate response models

Classical least squares can be strongly affected due to the inevitable occurrence of departures from its model assumptions, most notably those from the distributional assumptions. Robust estimators, on the other hand, will resist them. Unfortunately, the multiplicity of alternative robust regression estimators that have been suggested in the literature over the years is a source of confusion for practitioners of regression analysis. Moreover, little is known about their small-sample performance in the nonlinear regression setting, in particular on the chemical engineering field. A simulation study comparing six such estimators (namely LMS, LTS, LTD, MM-, ττ-, and LpLp-norm) together with the usual least squares estimator is presented. The results obtained provide guidance as to the choice of an appropriate estimator.