Robust Estimation in the Nonlinear Regression Model with Missing Responses

BIANCO, ANA MARIA; SPANO, PAULA MERCEDES

Punta del Este

Workshop; Escuela CIMPA-UNESCO: New trends in mathematical statistics research; 2012

In many situations the nature of the phenomenon of interest is intrinsically nonlinear and thus, the data must be fitted using a nonlinear model. Likewise, some responses may be missing at random. It is well known that, in this setting, the classical estimator of the regression parameters, which is based on least squares, is very sensitive to outliers. We study a family of simplified general M-estimators of the regression parameter in a nonlinear model with possible responses missing at random. Under mild conditions, this family of estimators turns out to be Fisher consistent, consistent and asymptotically normal. To study local robustness, their influence function is derived. By menans of Monte Carlo simulations we illustrate the finite sample behaviour of the proposed estimators in different settings in both contaminated and uncontaminated samples.