A Goodness-of-Fit Test for Independent Component Models in High Dimensions
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866914580611989504 |
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| author | Liu, Mingshuo Wang, Siyao Lopes, Miles E. |
| author_facet | Liu, Mingshuo Wang, Siyao Lopes, Miles E. |
| contents | Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_20099 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Goodness-of-Fit Test for Independent Component Models in High Dimensions Liu, Mingshuo Wang, Siyao Lopes, Miles E. Statistics Theory Methodology Independent component (IC) models are a standard tool for representing multivariate data in statistics, signal processing, and machine learning. Despite the extensive use of IC models, much less attention has been given to goodness-of-fit tests for assessing their compatibility with data. We develop the first goodness-of-fit test for IC models that is supported by a theoretical validity guarantee when the data dimension and sample size diverge proportionally. This is made possible by the fact that the test does not rely on a pre-whitening step, which often limits the applicability of other goodness-of-fit tests in high dimensions. Our theoretical analysis is complemented with numerical experiments that demonstrate the test's size control and power under a range of conditions. In addition, we provide examples involving gene-expression data to illustrate that the test has potential for effective diagnostic use in practice. |
| title | A Goodness-of-Fit Test for Independent Component Models in High Dimensions |
| topic | Statistics Theory Methodology |
| url | https://arxiv.org/abs/2605.20099 |