High Breakdown Point Estimators in Logistic Regression

Estimators with high finite sample breakdown points are of special interest in robust statistics. However, in contrast to estimation in linear regression models the breakdown point approach have not yet received much attention in logistic regression models. Although various robust estimators have been proposed in logistic regression models, their breakdown points are often not yet known. Here it is shown for logistic regression models with binary data that there is no estimator with a high finite sample breakdown point, provided the estimator has to fulfill a weak condition. However, in logistic regression models with large strata modifications of Rousseeuw’s least median of squares estimator and least trimmed squares estimator have finite sample breakdown points of approximately 1/2. Both estimators are strongly consistent under a large supermodel of the logistic regression model. Existing programs can be used to compute such estimates.