ROBUST NONLINEAR-REGRESSION ANALYSIS

In the linear regression problem M-estimators are frequently applied as an alternative to least squares estimators to obtain robustness, when there are outliers in the dependent variable. When we allow for nonlinear transformations of the variables (Young, 1981), the effects of outliers can still be large. In this paper it is shown that M-estimators can also be used for nonlinear multiple regression. Two types of M-estimators are used: the Huber and biweight estimator. Permutation tests are applied to obtain significance levels for the multiple correlation coefficients. Furthermore, an exploratory procedure is proposed, which is useful in finding out which tuning constant is optimal for the given problem. In a Monte Carlo study the stability of the different solutions and the influence of the outliers is examined by using the jack-knife. It was found that the biweight function was the most robust and eliminated the influence of the outliers.