Using conditional bias in principal component analysis for the evaluation of joint influence on the eigenvalues of the covariance matrix

Abstract

Influence Analysis in Principal Component Analysis has usually been tackled using the influence function [1] or local influence [2] approaches. The main objective of this paper is that of proposing influence diagnostics for the eigenvalues of the covariance matrix, that is, for the variance explained by the principal components, from a different angle: that of the conditional bias [3]. An approximation of the conditional bias of the simple eigenvalues of the sample covariance matrix is calculated under normality and some influence diagnostics are proposed. The study is carried by considering joint influence.