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Robust fitting of mixture regression models

Listed author(s):
  • Bai, Xiuqin
  • Yao, Weixin
  • Boyer, John E.
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    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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    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
    DOI: 10.1016/j.csda.2012.01.016
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    1. 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.
    2. Hennig, Christian, 2003. "Clusters, outliers, and regression: fixed point clusters," Journal of Multivariate Analysis, Elsevier, vol. 86(1), pages 183-212, July.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
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