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Robust fitting of mixture regression models

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Author Info

  • Bai, Xiuqin
  • Yao, Weixin
  • Boyer, John E.
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    Abstract

    The existing methods for fitting mixture regression models assume a normal distribution for error and then estimate the regression parameters by the maximum likelihood estimate (MLE). In this article, we demonstrate that the MLE, like the least squares estimate, is sensitive to outliers and heavy-tailed error distributions. We propose a robust estimation procedure and an EM-type algorithm to estimate the mixture regression models. Using a Monte Carlo simulation study, we demonstrate that the proposed new estimation method is robust and works much better than the MLE when there are outliers or the error distribution has heavy tails. In addition, the proposed robust method works comparably to the MLE when there are no outliers and the error is normal. A real data application is used to illustrate the success of the proposed robust estimation procedure.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0167947312000369
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    Bibliographic Info

    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 56 (2012)
    Issue (Month): 7 ()
    Pages: 2347-2359

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    Handle: RePEc:eee:csdana:v:56:y:2012:i:7:p:2347-2359

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    Web page: http://www.elsevier.com/locate/csda

    Related research

    Keywords: EM algorithm; Mixture regression models; Outliers; Robust regression;

    References

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    1. Neykov, N. & Filzmoser, P. & Dimova, R. & Neytchev, P., 2007. "Robust fitting of mixtures using the trimmed likelihood estimator," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 299-308, September.
    2. L. A. García-Escudero & A. Gordaliza & R. San Martín & S. Van Aelst & R. Zamar, 2009. "Robust linear clustering," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 301-318.
    3. Hennig, Christian, 2003. "Clusters, outliers, and regression: fixed point clusters," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 183-212, July.
    4. Yao, Weixin & Lindsay, Bruce G., 2009. "Bayesian Mixture Labeling by Highest Posterior Density," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 758-767.
    5. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    6. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    7. Müller, Christine H. & Garlipp, Tim, 2005. "Simple consistent cluster methods based on redescending M-estimators with an application to edge identification in images," Journal of Multivariate Analysis, Elsevier, vol. 92(2), pages 359-385, February.
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    Citations

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    Cited by:
    1. Song, Weixing & Yao, Weixin & Xing, Yanru, 2014. "Robust mixture regression model fitting by Laplace distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 128-137.
    2. Inmaculada Martinez‐Zarzoso & Antonello Maruotti, 2013. "The environmental Kuznets curve: functional form, time‐varying heterogeneity and outliers in a panel setting," Environmetrics, John Wiley & Sons, Ltd., vol. 24(7), pages 461-475, November.
    3. Shi, Jianhong & Chen, Kun & Song, Weixing, 2014. "Robust errors-in-variables linear regression via Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 84(C), pages 113-120.
    4. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.

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