IDEAS home Printed from https://ideas.repec.org/a/spr/testjl/v30y2021i2d10.1007_s11749-020-00725-z.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11749-020-00725-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11749-020-00725-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Jiahua Chen & Pengfei Li & Yuejiao Fu, 2012. "Inference on the Order of a Normal Mixture," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(499), pages 1096-1105, September.
    2. Xiang, Sijia & Yao, Weixin & Seo, Byungtae, 2016. "Semiparametric mixture: Continuous scale mixture approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 413-425.
    3. Mian Huang & Weixin Yao, 2012. "Mixture of Regression Models With Varying Mixing Proportions: A Semiparametric Approach," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 711-724, June.
    4. Bordes, Laurent & Chauveau, Didier & Vandekerkhove, Pierre, 2007. "A stochastic EM algorithm for a semiparametric mixture model," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5429-5443, July.
    5. 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.
    6. M. Levine & D. R. Hunter & D. Chauveau, 2011. "Maximum smoothed likelihood for multivariate mixtures," Biometrika, Biometrika Trust, vol. 98(2), pages 403-416.
    7. 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.
    8. Mian Huang & Runze Li & Shaoli Wang, 2013. "Nonparametric Mixture of Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 929-941, September.
    9. Li, Pengfei & Chen, Jiahua, 2010. "Testing the Order of a Finite Mixture," Journal of the American Statistical Association, American Statistical Association, vol. 105(491), pages 1084-1092.
    10. Wang, Shaoli & Huang, Mian & Wu, Xing & Yao, Weixin, 2016. "Mixture of functional linear models and its application to CO2-GDP functional data," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 1-15.
    11. Hu, Hao & Wu, Yichao & Yao, Weixin, 2016. "Maximum likelihood estimation of the mixture of log-concave densities," Computational Statistics & Data Analysis, Elsevier, vol. 101(C), pages 137-147.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    2. Sijia Xiang & Weixin Yao, 2020. "Semiparametric mixtures of regressions with single-index for model based 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. 14(2), pages 261-292, June.
    3. Sphiwe B. Skhosana & Salomon M. Millard & Frans H. J. Kanfer, 2023. "A Novel EM-Type Algorithm to Estimate Semi-Parametric Mixtures of Partially Linear Models," Mathematics, MDPI, vol. 11(5), pages 1-20, February.
    4. Mazo, Gildas & Averyanov, Yaroslav, 2019. "Constraining kernel estimators in semiparametric copula mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 170-189.
    5. Xue, Jiacheng & Yao, Weixin, 2022. "Machine Learning Embedded Semiparametric Mixtures of Regressions with Covariate-Varying Mixing Proportions," Econometrics and Statistics, Elsevier, vol. 22(C), pages 159-171.
    6. Marco Berrettini & Giuliano Galimberti & Saverio Ranciati, 2023. "Semiparametric finite mixture of regression models with Bayesian P-splines," 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(3), pages 745-775, September.
    7. Holzmann, Hajo & Schwaiger, Florian, 2016. "Testing for the number of states in hidden Markov models," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 318-330.
    8. Abbas Khalili & Farhad Shokoohi & Masoud Asgharian & Shili Lin, 2023. "Sparse estimation in semiparametric finite mixture of varying coefficient regression models," Biometrics, The International Biometric Society, vol. 79(4), pages 3445-3457, December.
    9. Hoshino Tadao & Yanagi Takahide, 2022. "Estimating marginal treatment effects under unobserved group heterogeneity," Journal of Causal Inference, De Gruyter, vol. 10(1), pages 197-216, January.
    10. Chauveau, Didier & Hoang, Vy Thuy Lynh, 2016. "Nonparametric mixture models with conditionally independent multivariate component densities," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 1-16.
    11. Kasahara Hiroyuki & Shimotsu Katsumi, 2012. "Testing the Number of Components in Finite Mixture Models," Global COE Hi-Stat Discussion Paper Series gd12-259, Institute of Economic Research, Hitotsubashi University.
    12. Hiroyuki Kasahara & Katsumi Shimotsu, 2017. "Testing the Order of Multivariate Normal Mixture Models," CIRJE F-Series CIRJE-F-1044, CIRJE, Faculty of Economics, University of Tokyo.
    13. Wichitchan, Supawadee & Yao, Weixin & Yang, Guangren, 2019. "Hypothesis testing for finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 180-189.
    14. 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.
    15. Xiaotian Zhu & David R. Hunter, 2019. "Clustering via finite nonparametric ICA mixture models," 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. 13(1), pages 65-87, March.
    16. Gildas Mazo, 2017. "A Semiparametric and Location-Shift Copula-Based Mixture Model," Journal of Classification, Springer;The Classification Society, vol. 34(3), pages 444-464, October.
    17. David Hunter & Derek Young, 2012. "Semiparametric mixtures of regressions," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 19-38.
    18. Jiali Zheng & Xiyang Wang, 2022. "Estimation for a Class of Semiparametric Pareto Mixture Densities," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 84(2), pages 609-627, August.
    19. Xiaotian Zhu & David R. Hunter, 2016. "Theoretical grounding for estimation in conditional independence multivariate finite mixture models," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 683-701, October.
    20. Michael Vogt & Matthias Schmid, 2021. "Clustering with statistical error control," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(3), pages 729-760, September.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:testjl:v:30:y:2021:i:2:d:10.1007_s11749-020-00725-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.