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2016 Affine-invariant rank tests for multivariate independence in independent component models
Hannu Oja, Davy Paindaveine, Sara Taskinen
Electron. J. Statist. 10(2): 2372-2419 (2016). DOI: 10.1214/16-EJS1174


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, à 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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Hannu Oja. Davy Paindaveine. Sara Taskinen. "Affine-invariant rank tests for multivariate independence in independent component models." Electron. J. Statist. 10 (2) 2372 - 2419, 2016.


Received: 1 January 2016; Published: 2016
First available in Project Euclid: 6 September 2016

zbMATH: 1346.62095
MathSciNet: MR3544291
Digital Object Identifier: 10.1214/16-EJS1174

Primary: 62G10, 62H15
Secondary: 62G35

Rights: Copyright © 2016 The Institute of Mathematical Statistics and the Bernoulli Society


Vol.10 • No. 2 • 2016
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