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Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models

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  • Marc Hallin
  • Simos Meintanis
  • Klaus Nordhausen

Abstract

We propose a family of tests of the validity of the assumptions underlying independent component analysis methods. The tests are formulated as L2–type procedures based on characteristic functions and involve weights; a proper choice of these weights and the estimation method for the mixing matrix yields consistent and affine-invariant tests. Due to the complexity of the asymptotic null distribution of the resulting test statistics, implementation is based on permutational and resampling strategies. This leads to distribution-free procedures regardless of whether these procedures are performed on the estimated independent components themselves or the componentwise ranks of their components. A Monte Carlo study involving various estimation methods for the mixing matrix, various weights, and a competing test based on distance covariance is conducted under the null hypothesis as well as under alternatives. A real-data application demonstrates the practical utility and effectiveness of the method.

Suggested Citation

  • Marc Hallin & Simos Meintanis & Klaus Nordhausen, 2024. "Consistent Distribution–Free Affine–Invariant Tests for the Validity of Independent Component Models," Working Papers ECARES 2024-04, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/368952
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    References listed on IDEAS

    as
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    Keywords

    Characteristic function; total independence; independent component model; rank test;
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