On consistency of the MLE under finite mixtures of location-scale distributions with a structural parameter
arXiv:2507.13764 · doi:10.1016/j.jspi.2018.05.003
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 . An extension of the strong consistency results to finite mixtures of multivariate elliptical distributions is also discussed.