Robust median estimator in logistic regression

This paper introduces a median estimator of the logistic regression parameters. It is defined as the classical L1L1-estimator applied to continuous data Z1,…,ZnZ1,…,Zn obtained by a statistical smoothing of the original binary logistic regression observations Y1,…,YnY1,…,Yn. Consistency and asymptotic normality of this estimator are proved. A method called enhancement is introduced which in some cases increases the efficiency of this estimator. Sensitivity to contaminations and leverage points is studied by simulations and compared in this manner with the sensitivity of some robust estimators previously introduced to the logistic regression. The new estimator appears to be more robust for larger sample sizes and higher levels of contamination.