Robust estimation in nonlinear regression and limited dependent variable models

Classical parametric estimation methods applied to nonlinear regression and limited-dependent-variable models are very sensitive to misspecification and data errors. On the other hand, semiparametric and nonparametric methods, which are not restricted by parametric assumptions, require more data and are less efficient. A third possible estimation approach is based on the theory of robust statistics, which builds upon parametric specification, but provides a methodology for designing misspecification-proof estimators. However, this concept, developed in statistics, has so far been applied almost exclusively to linear regression models. Therefore, I adapt some robust methods, such as least trimmed squares, to nonlinear and limited-dependent variable models. This paper presents the adapted robust estimators, proofs of their consistency, suitable computational methods, as well as examples of regression models which the proposed estimators can be applied to.