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Semiparametric mixtures of regressions with single-index for model based clustering

Author

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  • Sijia Xiang

    (Zhejiang University of Finance & Economics)

  • Weixin Yao

    (University of California)

Abstract

In this article, we propose two classes of semiparametric mixture regression models with single-index for model based clustering. Unlike many semiparametric/nonparametric mixture regression models that can only be applied to low dimensional predictors, the new semiparametric models can easily incorporate high dimensional predictors into the nonparametric components. The proposed models are very general, and many of the recently proposed semiparametric/nonparametric mixture regression models are indeed special cases of the new models. Backfitting estimates and the corresponding modified EM algorithms are proposed to achieve optimal convergence rates for both parametric and nonparametric parts. We establish the identifiability results of the proposed two models and investigate the asymptotic properties of the proposed estimation procedures. Simulation studies are conducted to demonstrate the finite sample performance of the proposed models. Two real data applications using the new models reveal some interesting findings.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:advdac:v:14:y:2020:i:2:d:10.1007_s11634-020-00392-w
    DOI: 10.1007/s11634-020-00392-w
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    References listed on IDEAS

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    1. 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.
    2. 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.
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    9. Wang, Shaoli & Yao, Weixin & Huang, Mian, 2014. "A note on the identifiability of nonparametric and semiparametric mixtures of GLMs," Statistics & Probability Letters, Elsevier, vol. 93(C), pages 41-45.
    10. Yao, Weixin & Lindsay, Bruce G., 2009. "Bayesian Mixture Labeling by Highest Posterior Density," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 758-767.
    11. Wang, Hansheng & Xia, Yingcun, 2008. "Sliced Regression for Dimension Reduction," Journal of the American Statistical Association, American Statistical Association, vol. 103, pages 811-821, June.
    12. Weixin Yao & Debmalya Nandy & Bruce G. Lindsay & Francesca Chiaromonte, 2019. "Covariate Information Matrix for Sufficient Dimension Reduction," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 114(528), pages 1752-1764, October.
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    14. Mian Huang & Runze Li & Hansheng Wang & Weixin Yao, 2014. "Estimating Mixture of Gaussian Processes by Kernel Smoothing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 32(2), pages 259-270, April.
    15. Wang, Qin & Yao, Weixin, 2012. "An adaptive estimation of MAVE," Journal of Multivariate Analysis, Elsevier, vol. 104(1), pages 88-100, February.
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    2. 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.

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