TICM-package: Testing the Validity of the Independent Component Model...

In TICM: Testing the Validity of the Independent Component Model Assumption

Testing the Validity of the Independent Component Model Assumption

Description

Description: Provides affine-invariant, distribution-free tests of multivariate independence, applied either directly to observed data or to estimated independent components. In the latter case, the procedures can be used to assess the validity of independent component models. The tests are based on L2-type distances between characteristic functions, with inference carried out using permutation or bootstrap resampling schemes. The methods are described in Hallin et al. (2024) <doi:10.48550/arXiv.2404.07632>.

Details

The TICM package implements characteristic-function based, L2-type procedures for (i) testing total multivariate independence in observed data and (ii) assessing the validity of an independent component model by testing mutual independence of estimated independent components.

The main user-facing functions are:

• ind_test: tests complete independence among the columns of a data matrix.

• icm_test: estimates independent components via ICA (e.g., JADE, FOBI, or FastICA) and then performs a total independence test to the estimated components to assess the validity of the independent component model.

• plot.ticm: diagnostic visualization of the estimated independent components returned by icm_test via a scatterplot matrix.

Both testing functions allow optional marginal score transformations ("Identity", "Rank", "VdW") and offer resampling-based inference using either permutation or bootstrap strategies to approximate p-values.

Typical workflow

1. Use ind_test to test whether the observed variables appear mutually independent.

2. Use icm_test to estimate independent components and test whether the resulting components are mutually independent (a diagnostic for the independent component model).

3. Use plot() on the ticm result for a quick visual check of pairwise dependence.

Author(s)

Klaus Nordhausen [aut, cre] (ORCID: <https://orcid.org/0000-0002-3758-8501>), Marc Hallin [aut] (ORCID: <https://orcid.org/0000-0002-6599-7409>), Simos Meintanis [aut] (ORCID: <https://orcid.org/0000-0003-4777-0486>)

Maintainer: Klaus Nordhausen <[e-mail]>

References

Hallin, M., Meintanis, S.G. and Nordhausen, K. (2024), Consistent distribution free affine invariant tests for the validity of independent component models. arXiv:2404.07632.

See Also

icm_test, ind_test

TICM documentation built on Feb. 12, 2026, 1:07 a.m.