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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| Schlagworte: | |
| Online-Zugang: | https://arxiv.org/abs/2404.07632 |
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| _version_ | 1866913310211833856 |
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| author | Hallin, Marc Meintanis, Simos G. Nordhausen, Klaus |
| author_facet | Hallin, Marc Meintanis, Simos G. Nordhausen, Klaus |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_07632 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Consistent Distribution Free Affine Invariant Tests for the Validity of Independent Component Models Hallin, Marc Meintanis, Simos G. Nordhausen, Klaus Methodology 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. |
| title | Consistent Distribution Free Affine Invariant Tests for the Validity of Independent Component Models |
| topic | Methodology |
| url | https://arxiv.org/abs/2404.07632 |