Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 10, Number 2 (2016), 2372-2419.
Affine-invariant rank tests for multivariate independence in independent component models
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.
Electron. J. Statist., Volume 10, Number 2 (2016), 2372-2419.
Received: January 2016
First available in Project Euclid: 6 September 2016
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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