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Robust fitting of mixture regression models

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

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.

Suggested Citation

  • Bai, Xiuqin & Yao, Weixin & Boyer, John E., 2012. "Robust fitting of mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 56(7), pages 2347-2359.
    • 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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    References listed on IDEAS

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    7. 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.
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    Cited by:

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    12. Luca Greco & Antonio Lucadamo & Claudio Agostinelli, 2021. "Weighted likelihood latent class linear regression," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(2), pages 711-746, June.
    13. Andrea Cerioli & Domenico Perrotta, 2014. "Robust clustering around regression lines with high density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 8(1), pages 5-26, March.
    14. Meng Li & Sijia Xiang & Weixin Yao, 2016. "Robust estimation of the number of components for mixtures of linear regression models," Computational Statistics, Springer, vol. 31(4), pages 1539-1555, December.
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    16. Li, Xiongya & Bai, Xiuqin & Song, Weixing, 2017. "Robust mixture multivariate linear regression by multivariate Laplace distribution," Statistics & Probability Letters, Elsevier, vol. 130(C), pages 32-39.
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    18. 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.
    19. P Alquier & M Gerber, 2024. "Universal robust regression via maximum mean discrepancy," Biometrika, Biometrika Trust, vol. 111(1), pages 71-92.
    20. Sangkon Oh & Byungtae Seo, 2023. "Merging Components in Linear Gaussian Cluster-Weighted Models," Journal of Classification, Springer;The Classification Society, vol. 40(1), pages 25-51, April.
    21. Atefeh Zarei & Zahra Khodadadi & Mohsen Maleki & Karim Zare, 2023. "Robust mixture regression modeling based on two-piece scale mixtures of normal distributions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 17(1), pages 181-210, March.
    22. 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.

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