Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when penalty is imposed on the ratios of the scale parameters - Mathematics > Statistics TheoryReport as inadecuate




Strong consistency of the maximum likelihood estimator for finite mixtures of location-scale distributions when penalty is imposed on the ratios of the scale parameters - Mathematics > Statistics Theory - Download this document for free, or read online. Document in PDF available to download.

Abstract: In finite mixtures of location-scale distributions, if there is no constraintor penalty on the parameters, then the maximum likelihood estimator does notexist because the likelihood is unbounded. To avoid this problem, we consider apenalized likelihood, where the penalty is a function of the minimum of theratios of the scale parameters and the sample size. It is shown that thepenalized maximum likelihood estimator is strongly consistent. We also analyzethe consistency of a penalized maximum likelihood estimator where the penaltyis imposed on the scale parameters themselves.



Author: Kentaro Tanaka

Source: https://arxiv.org/







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