A procedure for robust fitting in nonlinear regression

Outliers present more of a challenge in nonlinear than in linear models. As in the linear case, methods based on full-sample fits are not guaranteed to give larger residuals on the outliers than on inliers, and so identification methods starting from full-sample fits may fail. In addition, the fitting involves iterative calculation rather than closed-form explicit solutions, with the potential problems of convergence to local rather than global optima. The elemental set method, which has long been a fundamental tool in high breakdown linear fitting, is well suited to some nonlinear regression problems, providing an effective way of fitting the nonlinear equation, and providing the capability of doing so even in the face of large numbers of severe outliers. We discuss the basic elemental set method, and the nonlinear FAST-LTS approach, and propose a hybrid method with elemental searches preceding concentration steps. Crown