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2018 An MM algorithm for estimation of a two component semiparametric density mixture with a known component
Zhou Shen, Michael Levine, Zuofeng Shang
Electron. J. Statist. 12(1): 1181-1209 (2018). DOI: 10.1214/18-EJS1417

Abstract

We consider a semiparametric mixture of two univariate density functions where one of them is known while the weight and the other function are unknown. We do not assume any additional structure on the unknown density function. For this mixture model, we derive a new sufficient identifiability condition and pinpoint a specific class of distributions describing the unknown component for which this condition is mostly satisfied. We also suggest a novel approach to estimation of this model that is based on an idea of applying a maximum smoothed likelihood to what would otherwise have been an ill-posed problem. We introduce an iterative MM (Majorization-Minimization) algorithm that estimates all of the model parameters. We establish that the algorithm possesses a descent property with respect to a log-likelihood objective functional and prove that the algorithm, indeed, converges. Finally, we also illustrate the performance of our algorithm in a simulation study and apply it to a real dataset.

Citation

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Zhou Shen. Michael Levine. Zuofeng Shang. "An MM algorithm for estimation of a two component semiparametric density mixture with a known component." Electron. J. Statist. 12 (1) 1181 - 1209, 2018. https://doi.org/10.1214/18-EJS1417

Information

Received: 1 July 2017; Published: 2018
First available in Project Euclid: 28 March 2018

zbMATH: 06864489
MathSciNet: MR3780730
Digital Object Identifier: 10.1214/18-EJS1417

Subjects:
Primary: 62G07
Secondary: 62G99

JOURNAL ARTICLE
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Vol.12 • No. 1 • 2018
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