{"ID":2873916,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2509.05610","arxiv_id":"2509.05610","title":"On a surprising behavior of the likelihood ratio test in non-parametric mixture models","abstract":"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.","short_abstract":"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:...","url_abs":"https://arxiv.org/abs/2509.05610","url_pdf":"https://arxiv.org/pdf/2509.05610v1","authors":"[\"Yan Zhang\",\"Stanislav Volgushev\"]","published":"2025-09-06T06:13:29Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}