R-Estimation for Asymmetric Independent Component Analysis
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
(This abstract was borrowed from another version of this item.)
|Date of creation:||Apr 2013|
|Date of revision:|
|Publication status:||Published by:|
|Contact details of provider:|| Postal: Av. F.D., Roosevelt, 39, 1050 Bruxelles|
Phone: (32 2) 650 30 75
Fax: (32 2) 650 44 75
Web page: http://difusion.ulb.ac.be
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hallin, M. & Werker, B.J.M., 2003.
"Semiparametric efficiency, distribution-freeness and invariance,"
Other publications TiSEM
fe20db00-786a-4261-9999-6, Tilburg University, School of Economics and Management.
- Marc Hallin & Bas Werker, 2003. "Semiparametric efficiency, distribution-freeness, and invariance," ULB Institutional Repository 2013/2119, ULB -- Universite Libre de Bruxelles.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:eca:wpaper:2013/142876. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Benoit Pauwels)
If references are entirely missing, you can add them using this form.