Electronic Journal of Statistics

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

Hannu Oja, Davy Paindaveine, and Sara Taskinen

Full-text: Open access

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, 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.

Article information

Source
Electron. J. Statist., Volume 10, Number 2 (2016), 2372-2419.

Dates
Received: January 2016
First available in Project Euclid: 6 September 2016

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1473187647

Digital Object Identifier
doi:10.1214/16-EJS1174

Mathematical Reviews number (MathSciNet)
MR3544291

Zentralblatt MATH identifier
1346.62095

Subjects
Primary: 62G10: Hypothesis testing 62H15: Hypothesis testing
Secondary: 62G35: Robustness

Keywords
Distribution-free tests independent component models rank tests singular information matrices tests for multivariate independence uniform local asymptotic normality

Citation

Oja, Hannu; Paindaveine, Davy; Taskinen, Sara. Affine-invariant rank tests for multivariate independence in independent component models. Electron. J. Statist. 10 (2016), no. 2, 2372--2419. doi:10.1214/16-EJS1174. https://projecteuclid.org/euclid.ejs/1473187647


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