Statistica Sinica 18(2008), 581-599

CLASSIFICATION EFFICIENCIES FOR ROBUST

LINEAR DISCRIMINANT ANALYSIS

Christophe Croux$^1$, Peter Filzmoser$^2$ and Kristel Joossens$^1$

$^1$K.U. Leuven and $^2$Vienna University of Technology

Abstract: Linear discriminant analysis is typically carried out using Fisher's method. This method relies on the sample averages and covariance matrices computed from the different groups constituting the training sample. Since sample averages and covariance matrices are not robust, it has been proposed to use robust estimators of location and covariance instead, yielding a robust version of Fisher's method. In this paper relative classification efficiencies of the robust procedures with respect to the classical method are computed. Second-order influence functions appear to be useful for computing these classification efficiencies. It turns out that, when using an appropriate robust estimator, the loss in classification efficiency at the normal model remains limited. These findings are confirmed by finite sample simulations.

Key words and phrases: Classification efficiency, discriminant analysis, error rate, Fisher rule, influence function, robustness.