Estimation of Independent Component Analysis Systems

TL;DR

This paper introduces an optimal, computationally feasible estimator for Independent Component Analysis that overcomes previous challenges, does not require higher-order moments, and includes a useful specification test, demonstrated through simulations and macroeconomic applications.

Contribution

It extends existing ICA objective functions using continuum GMM, providing an estimator that is both asymptotically efficient and practical, with an integrated specification test.

Findings

Estimator outperforms GMM, JADE, and FastICA in simulations.

Method is effective in estimating Structural Vector Autoregressions.

Approach is computationally feasible and adaptable to sensor estimation.

Abstract

Although approaches to Independent Component Analysis (ICA) based on characteristic function seem theoretically elegant, they may suffer from implementational challenges because of numerical integration steps or selection of tuning parameters. Extending previously considered objective functions and leveraging results from the continuum Generalized Method of Moments of Carrasco and Florens (2000), I derive an optimal estimator that can take a tractable form and thus bypass these concerns. The method shares advantages with characteristic function approaches -- it does not require the existence of higher-order moments or parametric restrictions -- while retaining computational feasibility and asymptotic efficiency. The results are adapted to handle a possible first step that delivers estimated sensors. Finally, a by-product of the approach is a specification test that is valuable in many ICA applications. The method's effectiveness is illustrated through simulations, where the estimator outperforms efficient GMM, JADE, or FastICA, and an application to the estimation of Structural Vector Autoregressions (SVAR), a workhorse of the macroeconometric time series literature.