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A note on EM algorithm for mixture models

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  • Yao, Weixin

Abstract

Expectation–maximization (EM) algorithm has been used to maximize the likelihood function or posterior when the model contains unobserved latent variables. One main important application of EM algorithm is to find the maximum likelihood estimator for mixture models. In this article, we propose an EM type algorithm to maximize a class of mixture type objective functions. In addition, we prove the monotone ascending property of the proposed algorithm and discuss some of its applications.

Suggested Citation

  • Yao, Weixin, 2013. "A note on EM algorithm for mixture models," Statistics & Probability Letters, Elsevier, vol. 83(2), pages 519-526.
    • Handle: RePEc:eee:stapro:v:83:y:2013:i:2:p:519-526
    DOI: 10.1016/j.spl.2012.10.017
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    References listed on IDEAS

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    1. Linton, Oliver & Xiao, Zhijie, 2007. "A Nonparametric Regression Estimator That Adapts To Error Distribution Of Unknown Form," Econometric Theory, Cambridge University Press, vol. 23(3), pages 371-413, June.
    2. Ao Yuan & Jan G. De Gooijer, 2007. "Semiparametric Regression with Kernel Error Model," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 34(4), pages 841-869, December.
    3. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
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    Cited by:

    1. Weixin Yao & Longhai Li, 2014. "A New Regression Model: Modal Linear Regression," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(3), pages 656-671, September.
    2. Aman Ullah & Tao Wang & Weixin Yao, 2021. "Modal regression for fixed effects panel data," Empirical Economics, Springer, vol. 60(1), pages 261-308, January.
    3. Linton, Oliver & Xiao, Zhijie, 2019. "Efficient estimation of nonparametric regression in the presence of dynamic heteroskedasticity," Journal of Econometrics, Elsevier, vol. 213(2), pages 608-631.
    4. Aman Ullah & Tao Wang & Weixin Yao, 2022. "Nonlinear modal regression for dependent data with application for predicting COVID‐19," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 185(3), pages 1424-1453, July.
    5. 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.
    6. Chen, Yixin & Wang, Qin & Yao, Weixin, 2015. "Adaptive estimation for varying coefficient models," Journal of Multivariate Analysis, Elsevier, vol. 137(C), pages 17-31.
    7. Tao Wang, 2024. "Non‐parametric Estimator for Conditional Mode with Parametric Features," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 86(1), pages 44-73, February.

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