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Semiparametric mixture regression with unspecified error distributions

Author

Listed:
  • 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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