A1 Refereed original research article in a scientific journal

Affine-invariant rank tests for multivariate independence in independent component models



Authors: Oja H, Paindaveine D, Taskinen S

Publisher: INST MATHEMATICAL STATISTICS

Publication year: 2016

Journal: Electronic Journal of Statistics

Journal name in source: ELECTRONIC JOURNAL OF STATISTICS

Journal acronym: ELECTRON J STAT

Volume: 10

Issue: 2

First page : 2372

Last page: 2419

Number of pages: 48

ISSN: 1935-7524

eISSN: 1935-7524

DOI: https://doi.org/10.1214/16-EJS1174


Abstract
We consider the problem of testing for multivariate independence in independent component (IC) models. Under a symmetry assumption, we develop parametric and nonparametric (signed-rank) tests. Unlike in independent component analysis (ICA), we allow for the singular cases involving more than one Gaussian independent component. The proposed rank tests are based on componentwise signed ranks, a la Puri and Sen. Unlike the Puri and Sen tests, however, our tests (i) are affine-invariant and (ii) are, for adequately chosen scores, locally and asymptotically optimal (in the Le Cam sense) at prespecified densities. Asymptotic local powers and asymptotic relative efficiencies with respect to Wilks' LRT are derived. Finite-sample properties are investigated through a Monte-Carlo study.

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Last updated on 2024-26-11 at 15:43