Pair-perturbation influence functions and local influence in PCA

Abstract

The perturbation theory of an eigenvalue problem provides a useful tool for the sensitivity analysis in principal component analysis (PCA). However, single-perturbation diagnostics can suffer from masking effects. In this paper, we develop the pair-perturbation influence functions for the eigenvalues and eigenvectors of covariance matrices utilized in PCA to uncover the masked influential points. The relationship between the empirical pair-perturbation influence function and local influence in pairs is also investigated. Moreover, we propose an approach for determining cut points for influence function values in PCA, which has not been addressed yet. A simulation study and a specific data example are provided to illustrate the application of these approaches.