Strong consistency of MLE for finite mixtures of location-scale distributions when the ratios of the scale parameters are exponentially small
نویسنده
چکیده
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), 0 < d < 1, where n is the sample size.
منابع مشابه
Strong consistency of MLE for finite mixtures of location-scale distributions when the scale parameters are exponentially small
In a finite mixture of location-scale distributions maximum likelihood estimator does not exist because of the unboundedness of the likelihood function when the scale parameter of some mixture component approaches zero. In order to study the strong consistency of maximum likelihood estimator, we consider the case that the scale parameters of the component distributions are restricted from below...
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