Efficient independent component analysis

TL;DR

This paper introduces a semiparametric approach to independent component analysis (ICA) using B-spline approximations, achieving asymptotic efficiency and improved performance over traditional methods.

Contribution

It presents a novel semiparametric estimation method for ICA based on efficient score functions, enhancing accuracy and efficiency.

Findings

The proposed estimator is asymptotically efficient under moderate conditions.

Simulation results show better performance than standard ICA methods.

The method effectively utilizes B-spline approximations for estimation.

Abstract

Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have been developed, but in-depth analysis of asymptotic efficiency has not been available. We analyze ICA using semiparametric theories and propose a straightforward estimate based on the efficient score function by using B-spline approximations. The estimate is asymptotically efficient under moderate conditions and exhibits better performance than standard ICA methods in a variety of simulations.