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Robust mixture regression model fitting by Laplace distribution

Author

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  • Song, Weixing
  • Yao, Weixin
  • Xing, Yanru

Abstract

A robust estimation procedure for mixture linear regression models is proposed by assuming that the error terms follow a Laplace distribution. Using the fact that the Laplace distribution can be written as a scale mixture of a normal and a latent distribution, this procedure is implemented by an EM algorithm which incorporates two types of missing information from the mixture class membership and the latent variable. Finite sample performance of the proposed algorithm is evaluated by simulations. The proposed method is compared with other procedures, and a sensitivity study is also conducted based on a real data set.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:71:y:2014:i:c:p:128-137
    DOI: 10.1016/j.csda.2013.06.022
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    References listed on IDEAS

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    1. 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.
    2. 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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    2. Chun Yu & Weixin Yao & Guangren Yang, 2020. "A Selective Overview and Comparison of Robust Mixture Regression Estimators," International Statistical Review, International Statistical Institute, vol. 88(1), pages 176-202, April.
    3. Saverio Ranciati & Giuliano Galimberti & Gabriele Soffritti, 2019. "Bayesian variable selection in linear regression models with non-normal errors," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 28(2), pages 323-358, June.
    4. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    5. Hu, Hao & Yao, Weixin & Wu, Yichao, 2017. "The robust EM-type algorithms for log-concave mixtures of regression models," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 14-26.
    6. Nguyen, Hien D. & McLachlan, Geoffrey J. & Ullmann, Jeremy F.P. & Janke, Andrew L., 2016. "Laplace mixture autoregressive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 18-24.
    7. Wu, Qiang & Yao, Weixin, 2016. "Mixtures of quantile regressions," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 162-176.
    8. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    9. Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    10. Naderi, Mehrdad & Mirfarah, Elham & Wang, Wan-Lun & Lin, Tsung-I, 2023. "Robust mixture regression modeling based on the normal mean-variance mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 180(C).
    11. Yunlu Jiang & Guo-Liang Tian & Yu Fei, 2019. "A robust and efficient estimation method for partially nonlinear models via a new MM algorithm," Statistical Papers, Springer, vol. 60(6), pages 2063-2085, December.
    12. 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.
    13. 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.
    14. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    15. Ang Shan & Fengkai Yang, 2021. "Bayesian Inference for Finite Mixture Regression Model Based on Non-Iterative Algorithm," Mathematics, MDPI, vol. 9(6), pages 1-13, March.
    16. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    17. Francesco Dotto & Alessio Farcomeni & Luis Angel García-Escudero & Agustín Mayo-Iscar, 2017. "A fuzzy approach to robust regression clustering," 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. 11(4), pages 691-710, December.
    18. 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.
    19. 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.
    20. Kang-Ping Lu & Shao-Tung Chang, 2022. "Robust Switching Regressions Using the Laplace Distribution," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    21. Lu, Zhenqiu (Laura) & Zhang, Zhiyong, 2014. "Robust growth mixture models with non-ignorable missingness: Models, estimation, selection, and application," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 220-240.
    22. 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).

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