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Abstract:
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Maximum likelihood fitting of the logistic regression parameters can be affected greatly by atypical observations. Several robust alternatives have been proposed and implemented in statistical software packages. However, upon considering the model via the case-control viewpoint, it is clear that current techniques can exhibit poor behavior in many common situations. A new robust class of procedures is introduced. The estimates are constructed via a minimum-distance approach after identifying the model with a semiparametric biased sampling model. A particularly useful choice of distance measure is described via a semiparametric empirical characteristic function. These new approaches can be highly efficient, while remaining robust to small deviations in the model. Thus, they can be used to fit the logistic regression model, even in the presence of atypical observations.
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