The squared symmetric FastICA estimator

TL;DR

This paper introduces the squared symmetric FastICA, a modification of the FastICA algorithm, and demonstrates its superior asymptotic efficiency compared to traditional methods through theoretical analysis.

Contribution

The paper proposes the squared symmetric FastICA, deriving its asymptotic properties and showing it outperforms existing FastICA variants in efficiency.

Findings

Squared symmetric FastICA has better asymptotic efficiency.

The modification affects only the symmetric case, not the deflation-based FastICA.

Theoretical analysis confirms improved performance across various scenarios.

Abstract

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 a novel estimate with unknown properties is obtained. In the paper we review the classic deflation-based and symmetric FastICA approaches and contrast these with the new 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. Asymptotic variances of the unmixing matrix estimates are then used to compare their efficiencies for large sample sizes showing that the squared symmetric FastICA estimator outperforms the other two estimators in a wide variety of situations.