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Activity Number: 228
Type: Contributed
Date/Time: Monday, August 4, 2014 : 2:00 PM to 3:50 PM
Sponsor: IMS
Abstract #313683 View Presentation
Title: R-Estimation for Asymmetric Independent Component Analysis
Author(s): Chintan Mehta*+
Companies: Yale University
Keywords: ranks ; independent component analysis (ICA) ; local asymptotic normality (LAN) ; R-estimation ; robustness
Abstract:

Independent Component Analysis (ICA) recently has attracted attention in the statistical literature as an alternative to elliptical models. We focus here on estimating the model's mixing matrix. Traditional methods (FOBI, Kernel-ICA, FastICA) originating from the engineering literature have consistency that requires moment conditions without achieving any type of asymptotic efficiency. Those estimators with favorble robustness features tend to have unclear optimality properties. An efficient (signed-)rank-based approach has been proposed by Ilmonen and Paindaveine (2011) for the case of symmetric component densities that fail to be root-n consistent as soon as a single component density is asymmetric. In this paper, 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. Finally, we show, through finite-sample experiments and by an empirical exercise, that our methods also may provide excellent results in a context such as image analysis, where the basic assumptions of ICA are quite unlikely to hold.


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