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Chen, Jiahua (2016)
Publisher: The Institute of Mathematical Statistics
Languages: English
Types: Article
Subjects: Mathematics - Statistics Theory, penalized MLE, Nonparametric MLE, 62F12, Pfanzagl approach, identfiability, Kiefer–Wolfowitz approach

Classified by OpenAIRE into

arxiv: Statistics::Methodology, Statistics::Theory, Statistics::Computation
Identifiers:doi:10.1214/16-STS578
The large-sample properties of likelihood-based statistical inference under mixture models have received much attention from statisticians. Although the consistency of the nonparametric MLE is regarded as a standard conclusion, many researchers ignore the precise conditions required on the mixture model. An incorrect claim of consistency can lead to false conclusions even if the mixture model under investigation seems well behaved. Under a finite normal mixture model, for instance, the consistency of the plain MLE is often erroneously assumed in spite of recent research breakthroughs. This paper streamlines the consistency results for the nonparametric MLE in general, and in particular for the penalized MLE under finite normal mixture models.

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