The Annals of Statistics

Independent component analysis via nonparametric maximum likelihood estimation

Richard J. Samworth and Ming Yuan

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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.

Article information

Ann. Statist., Volume 40, Number 6 (2012), 2973-3002.

First available in Project Euclid: 8 February 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62G07: Density estimation

Blind source separation density estimation independent component analysis log-concave projection nonparametric maximum likelihood estimator


Samworth, Richard J.; Yuan, Ming. Independent component analysis via nonparametric maximum likelihood estimation. Ann. Statist. 40 (2012), no. 6, 2973--3002. doi:10.1214/12-AOS1060.

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