Sensitivity analysis in multivariate methods: Decomposition of an arbitrary influence into a finite number of components

Abstract

The influence function of the covariance matrix is decomposed into a finite number of components. This decomposition provides a useful tool to develop efficient methods for computing empirical influence curves related to various multivariate methods. It can also be used to characterize multivariate methods from the sensitivity perspective. A numerical example is given to demonstrate efficient computing and to characterize some procedures of exploratory factor analysis.

Keywords:

• sensitivity analysis
• influence function
• principal component analysis
• canonical correlation analysis
• factor analysis
• efficient computing
• characterization of multivariate methods