Affine-invariant rank tests for multivariate independence in independent component models
Oja, H., Paindaveine, D., & Taskinen, S. (2016). Affine-invariant rank tests for multivariate independence in independent component models. Electronic Journal of Statistics, 10 (2), 2372-2419. doi:10.1214/16-EJS1174
Published inElectronic Journal of Statistics
© the Authors, 2016. This is an open access article distributed under the terms of a Creative Commons License.
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.