Logistic Discrimination using Robust Estimators

Logistic regression is frequently used for classifying observations into two groups. Unfortunately there are often outlying observations in a data set, who might affect the estimated model and the associated classification error rate. In this paper, the effect of observations in the training sample on the error rate is studied by computing influence functions. It turns out that the usual influence function vanishes, and that the use of second order influence functions is appropriate. It is shown that using robust estimators in logistic discrimination strongly reduces the effect of outliers on the classification error rate. Furthermore, the second order influence function can be used as diagnostic tool to pinpoint outlying observations.