Title: Robust estimators for generalized linear models with a dispersion parameter,
Abstract: Highly robust and efficient estimators for the generalized linear model with
a dispersion parameter are proposed. The estimators are based on three steps.
In the first step the maximum rank correlation estimator is used to
consistently estimate the slopes up to a scale factor. In the second step, the
scale factor, the intercept, and the dispersion parameter are consistently
estimated using a MT-estimator of a simple regression model. The combined
estimator is highly robust but inefficient. Then, randomized quantile residuals
based on the initial estimators are used to detect outliers to be rejected and
to define a set S of observations to be retained. Finally, a conditional
maximum likelihood (CML) estimator given the observations in S is computed. We
show that, under the model, S tends to the complete sample for increasing
sample size. Therefore, the CML tends to the unconditional maximum likelihood
estimator. It is therefore highly efficient, while maintaining the high degree
of robustness of the initial estimator. The case of the negative binomial
regression model is studied in detail.