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Semiparametric mixture regression with unspecified error distributions

Author

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  • Yanyuan Ma

    (The Pennsylvania State University)

  • Shaoli Wang

    (Shanghai University of Finance and Economics)

  • Lin Xu

    (Zhejiang University of Finance and Economics)

  • Weixin Yao

    (University of California, Riverside)

Abstract

In fitting a mixture of linear regression models, normal assumption is traditionally used to model the error and then regression parameters are estimated by the maximum likelihood estimators (MLE). This procedure is not valid if the normal assumption is violated. By extending the semiparametric regression estimator proposed by Hunter and Young (J Nonparametr Stat 24:19–38, 2012a) which requires the component error densities to be the same (including homogeneous variance), we propose semiparametric mixture of linear regression models with unspecified component error distributions to reduce the modeling bias. We establish a more general identifiability result under weaker conditions than existing results, construct a class of new estimators, and establish their asymptotic properties. These asymptotic results also apply to many existing semiparametric mixture regression estimators whose asymptotic properties have remained unknown due to the inherent difficulties in obtaining them. Using simulation studies, we demonstrate the superiority of the proposed estimators over the MLE when the normal error assumption is violated and the comparability when the error is normal. Analysis of a newly collected Equine Infectious Anemia Virus data in 2017 is employed to illustrate the usefulness of the new estimator.

Suggested Citation

  • Yanyuan Ma & Shaoli Wang & Lin Xu & Weixin Yao, 2021. "Semiparametric mixture regression with unspecified error distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 429-444, June.
    • Handle: RePEc:spr:testjl:v:30:y:2021:i:2:d:10.1007_s11749-020-00725-z
    DOI: 10.1007/s11749-020-00725-z
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    References listed on IDEAS

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    8. Mian Huang & Weixin Yao & Shaoli Wang & Yixin Chen, 2018. "Statistical Inference and Applications of Mixture of Varying Coefficient Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 45(3), pages 618-643, September.
    9. Sijia Xiang & Weixin Yao, 2018. "Semiparametric mixtures of nonparametric regressions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(1), pages 131-154, February.
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    Cited by:

    1. Sangkon Oh & Byungtae Seo, 2024. "Semiparametric mixture of linear regressions with nonparametric Gaussian scale mixture errors," 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. 18(1), pages 5-31, March.
    2. Jiacheng Xue & Weixin Yao & Sijia Xiang, 2025. "Machine learning embedded EM algorithms for semiparametric mixture regression models," Computational Statistics, Springer, vol. 40(1), pages 205-224, January.
    3. Nam-Hwui Kim & Ryan P. Browne, 2024. "Flexible mixture regression with the generalized hyperbolic distribution," 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. 18(1), pages 33-60, March.

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