Robust Procedures for Nonlinear Models for Full and Incomplete Data

Linear models are one of the most popular models in Statistics. However, in many situations the nature of the phenomenon is intrinsically nonlinear and so, linear approximations are not valid and the data must be fitted using a nonlinear model. Besides, in some occasions the responses are incomplete and some of them are missing at random.

It is well known that, in this setting, the classical estimator of the regression parameter based on least squares is very sensitive to outliers. A family of general M-estimators is proposed to estimate the regression parameter in a nonlinear model. We give a unified approach to treat full data or data with missing responses. Under mild conditions, the proposed estimators are Fisher-consistent, consistent and asymptotically normal. To study local robustness, their influence function is also derived.

A family of robust tests based on a Wald-type statistic is introduced in order to check hypotheses that involve the regression parameter. Monte Carlo simulations illustrate the finite sample behaviour of the proposed procedures in different settings in contaminated and uncontaminated samples.