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Robust mixture regression using the t-distribution

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  • Yao, Weixin
  • Wei, Yan
  • Yu, Chun

Abstract

The traditional estimation of mixture regression models is based on the normal assumption of component errors and thus is sensitive to outliers or heavy-tailed errors. A robust mixture regression model based on the t-distribution by extending the mixture of t-distributions to the regression setting is proposed. However, this proposed new mixture regression model is still not robust to high leverage outliers. In order to overcome this, a modified version of the proposed method, which fits the mixture regression based on the t-distribution to the data after adaptively trimming high leverage points, is also proposed. Furthermore, it is proposed to adaptively choose the degrees of freedom for the t-distribution using profile likelihood. The proposed robust mixture regression estimate has high efficiency due to the adaptive choice of degrees of freedom.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:116-127
    DOI: 10.1016/j.csda.2013.07.019
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    Cited by:

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    17. 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.
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    19. Kang-Ping Lu & Shao-Tung Chang, 2022. "Robust Switching Regressions Using the Laplace Distribution," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    20. Gabriele Perrone & Gabriele Soffritti, 2023. "Seemingly unrelated clusterwise linear regression for contaminated data," Statistical Papers, Springer, vol. 64(3), pages 883-921, June.
    21. Kang-Ping Lu & Shao-Tung Chang, 2021. "Robust Algorithms for Change-Point Regressions Using the t -Distribution," Mathematics, MDPI, vol. 9(19), pages 1-28, September.
    22. Loup-Noé Lévy & Jérémie Bosom & Guillaume Guerard & Soufian Ben Amor & Marc Bui & Hai Tran, 2022. "DevOps Model Appproach for Monitoring Smart Energy Systems," Energies, MDPI, vol. 15(15), pages 1-27, July.
    23. Yang, Yu-Chen & Lin, Tsung-I & Castro, Luis M. & Wang, Wan-Lun, 2020. "Extending finite mixtures of t linear mixed-effects models with concomitant covariates," Computational Statistics & Data Analysis, Elsevier, vol. 148(C).
    24. 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.

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