The Deflation-Based FastICA Estimator: Statistical Analysis Revisited

This paper provides a rigorous statistical analysis of the deflation-based FastICA estimator, where the independent components (ICs) are extracted sequentially. The focus is on two aspects of the estimator: robustness against outliers as measured by the influence function (IF) and on its asymptotic relative efficiency (ARE) as measured by the ratio of the asymptotic variance of the FastICA w.r.t. the optimal maximum likelihood estimator (MLE). The derived compact closed-form expression of the IF reveals the vulnerability of the FastICA estimator to outliers regardless of the used nonlinearity. A cautionary finding is that even a moderate observation towards certain directions can render the estimator deficient in the sense that its separation performance degrades worse than a plain guess. The IF allows the derivation of a compact closed-form expression for the asymptotic covariance matrix of the FastICA estimator and subsequently its asymptotic relative efficiencies (AREs). The ARE figures calculated for some selected source distributions illustrate the fact that the order which the ICs are found is crucial as the accuracy of the previously extracted components can dominantly affect the accuracy of the successive deflation stages.