Sensitivity Analysis in Multivariate Methods: Influence Function, Cook's Local Influence and Perturbation Theory of Eigenvalue Problems

Abstract

We have studied sensitivity analysis in statistical models, in particular, multivariate statistical models such as quantification methods (correspondence analysis), principal component analysis, canonical correlation analysis, factor analysis and covariance structure analysis, since early 1980s. This article surveys major methodologies of sensitivity analysis, which we used during our studies, including influence functions, Cook's local influence analysis using normal curvature and perturbation theory of eigenvalue problems, and discuss some topics related to these methodologies.