Independent Component Analysis via Distance Covariance
成果类型：
Article
署名作者：
Matteson, David S.; Tsay, Ruey S.
署名单位：
Cornell University; University of Chicago
刊物名称：
JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
ISSN/ISSBN：
0162-1459
DOI：
10.1080/01621459.2016.1150851
发表日期：
2017
页码：
623-637
关键词：
摘要：
This article introduces a novel statistical framework for independent component analysis (ICA) of multivariate data. We propose methodology for estimating mutually independent components, and a versatile resampling-based procedure for inference, including misspecification testing. Independent components are estimated by combining a nonparametric probability integral transformation with a generalized non parametric whitening method based on distance covariance that simultaneously minimizes all forms of dependence among the components. We prove the consistency of our estimator under minimal regularity conditions and detail conditions for consistency under model misspecification, all while placing assumptions on the observations directly, not on the latent components. U statistics of certain Euclidean distances between sample elements are combined to construct a test statistic for mutually independent components. The proposed measures and tests are based on both necessary and sufficient conditions for mutual independence. We demonstrate the improvements of the proposed method over several competing methods in simulation studies, and we apply the proposed ICA approach to two real examples and contrast it with principal component analysis.