João A. Branco

Projection-pursuit approach to robust linear discriminant analysis

Discriminant analysis plays an important role in multivariate statistics as a prediction and classification method. It has been successfully applied in many fields of work and research. As it happens with other multivariate methods, discriminant analysis is highly vulnerable to the presence of outliers that commonly occur in many real world data sets. The lack of robustness of the classical estimators on which the linear discriminant function is based is a severe disadvantage and several authors have worked to find efficient ways to prevent the damage that outliers can cause. This paper focuses on the projection-pursuit approach to discriminant analysis. The projection-pursuit estimators are described and theoretical properties are deduced and their relevance is highlighted. These include Fisher consistency, affine equivariance, partial influence functions and asymptotic distributions. Application to real data and a simulation study reveal the robustness of the projection-pursuit approach. In both analyses the data relates to a large number of variables, a situation that is becoming common when new technology is applied to data gathering.

Projection pursuit approach to robust canonical correlation analysis

Projection pursuit techniques are used to build new robust estimators for the parameters of the canonical correlation model. A simulation study shows that for non-ideal data these estimators can perform as well as other robust estimators. However, they can have much higher breakdown points. This advantage makes these estimators the right choice for use with real data, where potential outlying observations are very frequent.