The Influence Function of Stahel-donoho Type Methods for Robust Covariance Estimation and Pca

Principal component analysis (PCA) is a popular technique to reduce the dimension of the data at hand. Since PCA is based on the empirical variance-covariance matrix, the estimates can be severely damaged by outliers. To reduce these effects, several robust methods were developed, mostly by replacing the classical variance-covariance matrix by a robust version. In this paper we focus on Stahel-Donoho type covariance estimators and on ROBPCA, a recent method for robust PCA. In this paper we derive their influence functions. They give us some theoretical insight in the robustness of the estimators and they allow us to compute asymptotic efficiencies. As an application we also derive the influence function of a robust partial least squares regression method based on robust covariance estimators.