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R-Estimation for Asymmetric Independent Component Analysis

Author

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  • Marc Hallin
  • Chintan Mehta

Abstract

Independent component analysis (ICA) recently has attracted much attention in the statistical literature as an appealing alternative to elliptical models. Whereas k -dimensional elliptical densities depend on one single unspecified radial density, however, k -dimensional independent component distributions involve k unspecified component densities. In practice, for given sample size n and dimension k , this makes the statistical analysis much harder. We focus here on the estimation, from an independent sample, of the mixing/demixing matrix of the model. Traditional methods (FOBI, Kernel-ICA, FastICA) mainly originate from the engineering literature. Their consistency requires moment conditions, they are poorly robust, and do not achieve any type of asymptotic efficiency. When based on robust scatter matrices, the two-scatter methods developed by Oja, Sirkia, and Eriksson in 2006 and Nordhausen, Oja, and Ollila in 2008 enjoy better robustness features, but their optimality properties remain unclear. The "classical semiparametric" approach by Chen and Bickel in 2006, quite on the contrary, achieves semiparametric efficiency, but requires the estimation of the densities of the k unobserved independent components. As a reaction, an efficient (signed-)rank-based approach was proposed by Ilmonen and Paindaveine in 2011 for the case of symmetric component densities. The performance of their estimators is quite good, but they unfortunately fail to be root- n consistent as soon as one of the component densities violates the symmetry assumption. In this article, using ranks rather than signed ranks, we extend their approach to the asymmetric case and propose a one-step R -estimator for ICA mixing matrices. The finite-sample performances of those estimators are investigated and compared to those of existing methods under moderately large sample sizes. Particularly good performances are obtained from a version involving data-driven scores taking into account the skew
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Suggested Citation

  • Marc Hallin & Chintan Mehta, 2013. "R-Estimation for Asymmetric Independent Component Analysis," Working Papers ECARES 2013-19, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/142876
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    References listed on IDEAS

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    1. Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
    2. Sirkku Pauliina Ilmonen & Davy Paindaveine, 2011. "Semiparametrically Efficient Inference Based on Signed Ranks in Symmetric Independent Component Models," Working Papers ECARES ECARES 2011-003, ULB -- Universite Libre de Bruxelles.
    3. Delphine Cassart & Marc Hallin & Davy Paindaveine, 2010. "On the estimation of cross-information quantities in rank-based inference," Working Papers ECARES ECARES 2010-010, ULB -- Universite Libre de Bruxelles.
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    Citations

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    Cited by:

    1. Jaromír Antoch & Michal Černý & Ryozo Miura, 2025. "R-estimation in linear models: algorithms, complexity, challenges," Computational Statistics, Springer, vol. 40(1), pages 405-439, January.
    2. Hallin, Marc & La Vecchia, Davide, 2020. "A Simple R-estimation method for semiparametric duration models," Journal of Econometrics, Elsevier, vol. 218(2), pages 736-749.
    3. Bernd Funovits, 2019. "Identification and Estimation of SVARMA models with Independent and Non-Gaussian Inputs," Papers 1910.04087, arXiv.org.
    4. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    5. Lee, Seonjoo & Shen, Haipeng & Truong, Young, 2021. "Sampling properties of color Independent Component Analysis," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    6. Funovits, Bernd, 2024. "Identifiability and estimation of possibly non-invertible SVARMA Models: The normalised canonical WHF parametrisation," Journal of Econometrics, Elsevier, vol. 241(2).
    7. Jari Miettinen & Katrin Illner & Klaus Nordhausen & Hannu Oja & Sara Taskinen & Fabian J. Theis, 2016. "Separation of Uncorrelated Stationary time series using Autocovariance Matrices," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(3), pages 337-354, May.
    8. Piotr Zwiernik & Geert Mesters, 2022. "Non-Independent Components Analysis," Working Papers 1358, Barcelona School of Economics.
    9. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2017. "Identification and estimation of non-Gaussian structural vector autoregressions," Journal of Econometrics, Elsevier, vol. 196(2), pages 288-304.
    10. Hallin, M. & Werker, B.J.M. & van den Akker, R., 2015. "Optimal Pseudo-Gaussian and Rank-based Tests of the Cointegration Rank in Semiparametric Error-correction Models," Discussion Paper 2015-001, Tilburg University, Center for Economic Research.

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    Keywords

    independent component analysis (ICA); local asymptotic normality (LAN); ranks; R-Estimation; Robustness;
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