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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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    2. 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.

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