Robust tests in generalized linear models with missing responses

In many situations, data follow a generalized linear model in which the mean of the responses is modelled, through a link function, linearly on the covariates. In this paper, robust estimators for the regression parameter are considered in order to build test statistics for this parameter when missing data occur in the responses. We derive the asymptotic behaviour of the robust estimators for the regression parameter under the null hypothesis and under contiguous alternatives in order to obtain that of the robust Wald test statistics. Their influence function is also studied. A simulation study allows to compare the behaviour of the classical and robust tests, under different contamination schemes. The procedure is also illustrated analysing a real data set.