Algorithms for robust nonlinear regression with heteroscedastic errors

Nonlinear regression algorithms were compared by Monte-Carlo simulations when the measurement error was dependent on the measured values (heteroscedasticity) and possibly contaminated with outliers. The tested least-squares (LSQ) algorithms either required user-supplied weights to accommodate heteroscedasticity or the weights were estimated within the procedures. Robust versions of the LSQ algorithms, namely robust iteratively reweighted (IRR) and least absolute value (LAV) regressions, were also considered. The comparisons were based on the efficiency of the estimated parameters and their resistance to outliers. Based on these criteria, among the tested LSQ algorithms, extended least squares (ELSQ) was found to be the most reliable. The IRR versions of these algorithms were slightly more efficient than the LAV versions when there were no outliers but they provided weaker protection to outliers than the LAV variants.