The squared symmetric FastICA estimator

In this paper we study the theoretical properties of the deflation-based FastICA method, the original symmetric FastICA method, and a modified symmetric FastICA method, here called the squared symmetric FastICA. This modification is obtained by replacing the absolute values in the FastICA objective function by their squares. In the deflation-based case this replacement has no effect on the estimate since the maximization problem stays the same. However, in the symmetric case we obtain a different estimate which has been mentioned in the literature, but its theoretical properties has not been studied at all. In the paper we review the classic deflation-based and symmetric FastICA approaches and contrast these with the squared symmetric version of FastICA. We find the estimating equations and derive the asymptotical properties of the squared symmetric FastICA estimator with an arbitrary choice of nonlinearity. This allows the main contribution of the paper, i.e., efficiency comparison of the estimates in a wide variety of situations using ∗Corresponding author Email addresses: [email protected] (Jari Miettinen), [email protected] (Klaus Nordhausen), [email protected] (Hannu Oja), [email protected] (Sara Taskinen), @utu.fi (Joni Virta) Preprint submitted to Signal Processing August 10, 2016 asymptotic variances of the unmixing matrix estimates.