Robust inference for nonlinear regression models

A family of weighted estimators of the regression parameter under a nonlinear model is introduced. The proposed weighted estimators are computed through a four-step MM-procedure, and the given approach allows for possible missing responses. Under mild conditions, the proposed estimators turn to be consistent and asymptotically normal. A robust Wald-type test statistic based on this family of estimators is also provided, and its asymptotic distribution is derived under the null and contiguous hypotheses. The local robustness of the proposed procedures is studied via the influence function analysis, and the finite sample behaviour of the estimators and tests is investigated through a Monte Carlo study in different contaminated scenarios. An application to an environmental data set illustrates the procedure.