Fourth Moments and Independent Component Analysis

TL;DR

This paper analyzes the statistical properties of fourth-moment based estimators in independent component analysis, comparing their asymptotic efficiencies and providing insights into their performance.

Contribution

It introduces a detailed theoretical analysis of fourth-moment based ICA estimators, deriving their asymptotic properties and comparing their efficiencies.

Findings

JADE and symmetric FastICA generally outperform other estimators in asymptotic variance.

The paper provides explicit estimation algorithms and asymptotic analysis for fourth-moment based ICA.

It enhances understanding of the statistical behavior of popular ICA estimation methods.

Abstract

In independent component analysis it is assumed that the components of the observed random vector are linear combinations of latent independent random variables, and the aim is then to find an estimate for a transformation matrix back to these independent components. In the engineering literature, there are several traditional estimation procedures based on the use of fourth moments, such as FOBI (fourth order blind identification), JADE (joint approximate diagonalization of eigenmatrices), and FastICA, but the statistical properties of these estimates are not well known. In this paper various independent component functionals based on the fourth moments are discussed in detail, starting with the corresponding optimization problems, deriving the estimating equations and estimation algorithms, and finding asymptotic statistical properties of the estimates. Comparisons of the asymptotic variances of the estimates in wide independent component models show that in most cases JADE and the symmetric version of FastICA perform better than their competitors.