Open Access
December 2012 Independent component analysis via nonparametric maximum likelihood estimation
Richard J. Samworth, Ming Yuan
Ann. Statist. 40(6): 2973-3002 (December 2012). DOI: 10.1214/12-AOS1060


Independent Component Analysis (ICA) models are very popular semiparametric models in which we observe independent copies of a random vector $X=AS$, where $A$ is a non-singular matrix and $S$ has independent components. We propose a new way of estimating the unmixing matrix $W=A^{-1}$ and the marginal distributions of the components of $S$ using nonparametric maximum likelihood. Specifically, we study the projection of the empirical distribution onto the subset of ICA distributions having log-concave marginals. We show that, from the point of view of estimating the unmixing matrix, it makes no difference whether or not the log-concavity is correctly specified. The approach is further justified by both theoretical results and a simulation study.


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Richard J. Samworth. Ming Yuan. "Independent component analysis via nonparametric maximum likelihood estimation." Ann. Statist. 40 (6) 2973 - 3002, December 2012.


Published: December 2012
First available in Project Euclid: 8 February 2013

zbMATH: 1296.62084
MathSciNet: MR3097966
Digital Object Identifier: 10.1214/12-AOS1060

Primary: 62G07

Keywords: blind source separation , Density estimation , Independent component analysis , log-concave projection , nonparametric maximum likelihood estimator

Rights: Copyright © 2012 Institute of Mathematical Statistics

Vol.40 • No. 6 • December 2012
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