On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter

Fuente: arXiv
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Auteurs principaux: Liu, Guanfu, Li, Pengfei, Liu, Yukun, Pu, Xiaolong
Format: Preprint
Publié: 2025
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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