On a surprising behavior of the likelihood ratio test in non-parametric mixture models
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912574323294208 |
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| author | Zhang, Yan Volgushev, Stanislav |
| author_facet | Zhang, Yan Volgushev, Stanislav |
| contents | We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space. For Gaussian location mixtures and Poisson mixtures, we show a surprising result: the non-parametric likelihood ratio test statistic converges to a tight limit if and only if the null distribution is a finite mixture, and diverges to infinity otherwise. We further demonstrate that the likelihood ratio test diverges for a fairly general class of distributions when the null mixing distribution is not finitely discrete. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05610 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a surprising behavior of the likelihood ratio test in non-parametric mixture models Zhang, Yan Volgushev, Stanislav Statistics Theory We study the likelihood ratio test in general mixture models where the base density is parametric, the null is a known fixed mixing distribution, and the alternative is a general mixing distribution supported on a bounded parameter space. For Gaussian location mixtures and Poisson mixtures, we show a surprising result: the non-parametric likelihood ratio test statistic converges to a tight limit if and only if the null distribution is a finite mixture, and diverges to infinity otherwise. We further demonstrate that the likelihood ratio test diverges for a fairly general class of distributions when the null mixing distribution is not finitely discrete. |
| title | On a surprising behavior of the likelihood ratio test in non-parametric mixture models |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2509.05610 |