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Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models

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  • Yichen Qin
  • Carey E. Priebe

Abstract

We introduce a maximum L q -likelihood estimation (ML q E) of mixture models using our proposed expectation-maximization (EM) algorithm, namely the EM algorithm with L q -likelihood (EM-L q ). Properties of the ML q E obtained from the proposed EM-L q are studied through simulated mixture model data. Compared with the maximum likelihood estimation (MLE), which is obtained from the EM algorithm, the ML q E provides a more robust estimation against outliers for small sample sizes. In particular, we study the performance of the ML q E in the context of the gross error model, where the true model of interest is a mixture of two normal distributions, and the contamination component is a third normal distribution with a large variance. A numerical comparison between the ML q E and the MLE for this gross error model is presented in terms of Kullback--Leibler (KL) distance and relative efficiency.

Suggested Citation

  • Yichen Qin & Carey E. Priebe, 2013. "Maximum L q -Likelihood Estimation via the Expectation-Maximization Algorithm: A Robust Estimation of Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 914-928, September.
    • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:914-928
    DOI: 10.1080/01621459.2013.787933
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    Cited by:

    1. Pietro Coretto & Christian Hennig, 2016. "Robust Improper Maximum Likelihood: Tuning, Computation, and a Comparison With Other Methods for Robust Gaussian Clustering," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1648-1659, October.
    2. Yeşim Güney & Y. Tuaç & Ş. Özdemir & O. Arslan, 2021. "Conditional maximum Lq-likelihood estimation for regression model with autoregressive error terms," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(1), pages 47-74, January.
    3. Nelson, Kenric P., 2022. "Independent Approximates enable closed-form estimation of heavy-tailed distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 601(C).
    4. Xu, Lin & Xiang, Sijia & Yao, Weixin, 2019. "Robust maximum Lq-likelihood estimation of joint mean–covariance models for longitudinal data," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 397-411.

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