Article ID Journal Published Year Pages File Type
11020288 Journal of Statistical Planning and Inference 2019 16 Pages PDF
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.
Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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