{"ID":2893018,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.13764","arxiv_id":"2507.13764","title":"On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter","abstract":"We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale distributions with a structural parameter. The consistency results do not require the parameter space of location and scale to be compact. We illustrate the results by applying them to finite mixtures of location-scale distributions with the component density function being one of the commonly used density functions: normal, logistic, extreme-value, or $t$. An extension of the strong consistency results to finite mixtures of multivariate elliptical distributions is also discussed.","short_abstract":"We provide a general and rigorous proof for the strong consistency of maximum likelihood estimators of the cumulative distribution function of the mixing distribution and structural parameter under finite mixtures of location-scale distributions with a structural parameter. The consistency results do not require the pa...","url_abs":"https://arxiv.org/abs/2507.13764","url_pdf":"https://arxiv.org/pdf/2507.13764v1","authors":"[\"Guanfu Liu\",\"Pengfei Li\",\"Yukun Liu\",\"Xiaolong Pu\"]","published":"2025-07-18T09:16:55Z","proceeding":"math.ST","tasks":"[\"math.ST\"]","methods":"[]","has_code":false}