Inference for robust canonical variate analysis

Abstract

We consider the problem of optimally separating two multivariate populations. Robust linear discriminant rules can be obtained by replacing the empirical means and covariance in the classical discriminant rules by S or MM-estimates of location and scatter. We propose to use a fast and robust bootstrap method to obtain inference for such a robust discriminant analysis. This is useful since classical bootstrap methods may be unstable as well as extremely time-consuming when robust estimates such as S or MM-estimates are involved. In particular, fast and robust bootstrap can be used to investigate which variables contribute significantly to the canonical variate, and thus the discrimination of the classes. Through bootstrap, we can also examine the stability of the canonical variate. We illustrate the method on some real data examples.