INDEPENDENT COMPONENT ANALYSIS VIA NONPARAMETRIC MAXIMUM LIKELIHOOD ESTIMATION

• 成果类型: Article
• 署名作者: Samworth, Richard J.; Yuan, Ming
• 署名单位: University of Cambridge; University System of Georgia; Georgia Institute of Technology
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• DOI: 10.1214/12-AOS1060
• 发表日期: 2012
• 页码: 2973-3002
• 关键词: ica; distributions

摘要

Independent Component Analysis (ICA) models are very popular semi-parametric 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.