A robust conditional maximum likelihood estimator for generalized linear models with a dispersion parameter
- Marazzi, Alfio Natale
- Valdora, Marina Silvia
- Yohai, Victor Jaime
- Amiguet, Michael
DOIAbstract
Highly robust and efficient estimators for generalized linear models 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. The scale factor, the intercept, and the dispersion parameter are robustly estimated using a simple regression model. Then, randomized quantile residuals based on the initial estimators are used to define a region S such that observations out of S are considered as outliers. Finally, a conditional maximum likelihood (CML) estimator given the observations in S is computed. We show that, under the model, S tends to the whole space for increasing sample size. Therefore, th...
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