A robust principal component analysis

Abstract

A robust principal component analysis for samples from a bivariate distribution function is described. The method is based on robust estimators for dispersion in the univariate case along with a certain linearization of the bivariate structure. Besides the continuity of the functional defining the direction of the suitably modified principal axis, we prove consistency of the corresponding sequence of estimators. Asymptotic normality is established under some additional conditions.Principal component robustness robust estimator for dispersion linearization