Open Access
February 2017 Consistency of the MLE under Mixture Models
Jiahua Chen
Statist. Sci. 32(1): 47-63 (February 2017). 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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Jiahua Chen. "Consistency of the MLE under Mixture Models." Statist. Sci. 32 (1) 47 - 63, February 2017.


Published: February 2017
First available in Project Euclid: 6 April 2017

zbMATH: 06946263
MathSciNet: MR3634306
Digital Object Identifier: 10.1214/16-STS578

Keywords: identfiability , Kiefer–Wolfowitz approach , nonparametric MLE , penalized MLE , Pfanzagl approach

Rights: Copyright © 2017 Institute of Mathematical Statistics

Vol.32 • No. 1 • February 2017
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