On the Consistency of a Class of Nonlinear Regression Estimators

In this paper, we study conditions sufficient for strong consistency of a class of estimators of parameters of nonlinear regression models. The study considers continuous functions depending on a vector of parameters and a set of random regressors. The estimators chosen are minimizers of a generalized form of the signed-rank norm. The generalization allows us to make consistency statements about minimizers of a wide variety of norms including the L-1 and L-2 norms. By implementing trimming, it is shown that high breakdown estimates can be obtained based on the proposed dispersion function.