Robust linear discriminant analysis using S-estimators

The authors consider a robust linear discriminant function based on high breakdown location and covariance matrix estimators. They derive influence functions for the estimators of the parameters of the discriminant function and for the associated classification error. The most B-robust estimator is determined within the class of multivariate S-estimators. This estimator, which minimizes the maximal influence that an outlier can have on the classification error, is also the most B-robust location S-estimator. A comparison of the most B-robust estimator with the more familiar Biweight S-estimator is made.