Comparative Study of Robust Estimators Based on a Sensitivity Coefficient in Principal Component Analysis

This work is devoted to robust principal component analysis (PCA). We give a comparison between some multivariate estimators of location and scatter by computing the influence functions of the sensitivity coefficient ρ corresponding to these estimators, and the mean squared error (MSE) of estimators of ρ. The coefficient ρ measures the closeness between the subspaces spanned by the initial eigenvectors and their corresponding version derived from an infinitesimal perturbation of the data distribution.