## 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

Hannu Oja, Davy Paindaveine, and Sara Taskinen

#### 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