Implementing the Bianco and Yohai estimator for logistic regression

In 1996, Bianco and Yohai proposed a highly robust estimation procedure in the logistic regression model. The theoretical results they obtain were very promising. In this paper we complement their study by providing a fast and stable algorithm to compute this estimator. Moreover, we derive criteria for the existence of the estimator at finite samples and discuss the problem of the selection of the loss-function. Many other robust estimators have been introduced in logistic regression, some of these being standard available in some statistical softwares. We compare the performance of these estimators with respect to the estimator of Bianco and Yohai. We also look into the advantages of an extra weighting step.