Influence functions and local influence in linear discriminant analysis

The perturbation theory provides a useful tool for the sensitivity analysis in linear discriminant analysis (LDA). Though some influence functions by single perturbation and local influence in LDA have been discussed in literature, we propose yet another influence function inspired by Critchley [1985. Influence in principal component analysis. Biometrika 72, 627-636], called the deleted empirical influence function, as an alternative approach for the influence analysis in LDA. It is well-known that single-perturbation diagnostics can suffer from the masking effect. Hence in this paper we also develop the pair-perturbation influence functions to detect the masked influential points. The comparisons between pair-perturbation influence functions and local influences in pairs in LDA are also investigated. Finally, two examples are provided to illustrate the results of these approaches.