Robust inference in generalized partially linear models

In many situations, data follow a generalized partly linear model in which the mean of the responses is modeled, through a link function, linearly on some covariates and nonparametrically on the remaining ones. A new class of robust estimates for the smooth function [eta], associated to the nonparametric component, and for the parameter , related to the linear one, is defined. The robust estimators are based on a three-step procedure, where large values of the deviance or Pearson residuals are bounded through a score function. These estimators allow us to make easier inferences on the regression parameter and also improve computationally those based on a robust profile likelihood approach. The resulting estimates of turn out to be root-n consistent and asymptotically normally distributed. Besides, the empirical influence function allows us to study the sensitivity of the estimators to anomalous observations. A robust Wald test for the regression parameter is also provided. Through a Monte Carlo study, the performance of the robust estimators and the robust Wald test is compared with that of the classical ones.