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. This sensitivity is addressed by the theory of robust statistics which builds upon parametric specification, but provides methodology for designing misspecification-proof estimators by allowing for various "departures" of subsets of the data. 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 and proofs of their consistency. I also discuss several important examples of regression models which the proposed estimators can be applied to as well as suitable computational methods.
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