Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small

Details Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small

2006-09-25

arxiv.org/abs/math/0609678v2

Mathematics

Statistics Theory

11 pages, 2 figures. This paper is superseded by arXiv:0710.2183

Scientific paper

In finite mixtures of location-scale distributions, if there is no constraint on the parameters then the maximum likelihood estimate does not exist. But when the ratios of the scale parameters are restricted appropriately, the maximum likelihood estimate exists. We prove that the maximum likelihood estimator (MLE) is strongly consistent, if the ratios of the scale parameters are restricted from below by $\exp(-n^{d}), 0 < d < 1 $, where $n$ is the sample size.

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