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Howard D. Bondell, Minimum distance estimation for the logistic regression model, Biometrika, Volume 92, Issue 3, September 2005, Pages 724–731, https://doi.org/10.1093/biomet/92.3.724
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Abstract
It is well known that the maximum likelihood fit of the logistic regression parameters can be greatly affected by atypical observations. Several robust alternatives have been proposed. However, if we consider the model from the case-control viewpoint, it is clear that current techniques can exhibit poor behaviour in many common situations. A new robust class of estimation procedures is introduced. The estimators are constructed via a minimum distance approach after identifying the model with a semiparametric biased sampling model. The approach is developed under the case-control sampling scheme, yet is shown to be applicable under prospective sampling as well. A weighted Cramér–von Mises distance is used as an illustrative example of the methodology.