Robustness of classification rules that incorporate additional information

The discrimination problem for two normal populations with the same covariance matrix when additional information on the population is available is considered. A study of the robustness properties against training sample contamination of classification rules that incorporate this additional information is performed. These rules have received recently attention where their total misclassification probability (TMP) is proved to be lower than Fisher's linear discriminant rule. The results of a simulation study on the TMP which compares the behaviour of the new rules against Fisher's rule and some of its robustified versions under different types of contamination are presented. These results show that the rules that incorporate the additional information not only have lower TMP, but they also prevent against some types of contamination. In order to achieve prevention from all types of contamination a robustifed version of these rules is recommended.