The Performance of Classical and Robust Logistic Regression Estimators in the Presence of Outliers

It is now evident that the estimation of logistic regression parameters, using Maximum Likelihood Estimator (MLE), suffers a huge drawback in the presence of outliers. An alternative approach is to use robust logistic regression estimators, such as Mallows type leverage dependent weights estimator (MALLOWS), Conditionally Unbiased Bounded Influence Function estimator (CUBIF), Bianco and Yohai estimator (BY), and Weighted Bianco and Yohai estimator (WBY). This paper investigates the robustness of the preceding robust estimators by using real data sets and Monte Carlo simulations. The results indicate that the MLE behaves poorly in the presence of outliers. On the other hand, the WBY estimator is more efficient than the other existing robust estimators. Thus, it is suggested that the WBY estimator be employed when outliers are present in the data to obtain a reliable estimate.