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Maximum likelihood estimation of the mixture of log-concave densities

Author

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  • Hu, Hao
  • Wu, Yichao
  • Yao, Weixin

Abstract

Finite mixture models are useful tools and can be estimated via the EM algorithm. A main drawback is the strong parametric assumption about the component densities. In this paper, a much more flexible mixture model is considered, which assumes each component density to be log-concave. Under fairly general conditions, the log-concave maximum likelihood estimator (LCMLE) exists and is consistent. Numeric examples are also made to demonstrate that the LCMLE improves the clustering results while comparing with the traditional MLE for parametric mixture models.

Suggested Citation

  • Hu, Hao & Wu, Yichao & Yao, Weixin, 2016. "Maximum likelihood estimation of the mixture of log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 137-147.
    • Handle: RePEc:eee:csdana:v:101:y:2016:i:c:p:137-147
    DOI: 10.1016/j.csda.2016.03.002
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    References listed on IDEAS

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    1. Cule, Madeleine & Gramacy, Robert B. & Samworth, Richard, 2009. "LogConcDEAD: An R Package for Maximum Likelihood Estimation of a Multivariate Log-Concave Density," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 29(i02).
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    Cited by:

    1. Chun Yu & Weixin Yao & Guangren Yang, 2020. "A Selective Overview and Comparison of Robust Mixture Regression Estimators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 176-202, April.
    2. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    3. Minerva Mukhopadhyay & Didong Li & David B. Dunson, 2020. "Estimating densities with non‐linear support by using Fisher–Gaussian kernels," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(5), pages 1249-1271, December.
    4. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    5. Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.

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