On the robustness of the deflation-based FastICA estimator

Abstract

This paper provides a rigorous statistical robustness analysis of the deflation-based FastICA estimator by deriving a compact closed form expression for its influence function (IF). The IF reveals the vulnerability of the FastICA estimator to outliers regardless of the used non-linearity. A cautionary finding is that even a moderate outlier towards certain directions can render the estimator deficient, i.e. having a separation performance worse than a plain guess. Based on the IF, a novel compact closed-form expression of the asymptotic covariance matrix of the FastICA estimator is also derived.