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

Marc Hallin, Simos Meintanis and Klaus Nordhausen

No 2024-04, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

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.

Keywords: Characteristic function; total independence; independent component model; rank test (search for similar items in EconPapers)
Pages: 56 p.
Date: 2024-02
New Economics Papers: this item is included in nep-dcm and nep-ecm
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