On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909694833983488 |
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| author | Liu, Guanfu Li, Pengfei Liu, Yukun Pu, Xiaolong |
| author_facet | Liu, Guanfu Li, Pengfei Liu, Yukun Pu, Xiaolong |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_13764 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter Liu, Guanfu Li, Pengfei Liu, Yukun Pu, Xiaolong Statistics Theory 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. |
| title | On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2507.13764 |