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arXiv · 2507.13764

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

Guanfu Liu·Pengfei Li·Yukun Liu·Xiaolong Pu
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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.

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Guanfu Liu, Pengfei Li, Yukun Liu, Xiaolong Pu. 2025-07-18. On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter. https://doi.org/10.1016/j.jspi.2018.05.003

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