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Mixture of Regression Models With Varying Mixing Proportions: A Semiparametric Approach

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  • Mian Huang
  • Weixin Yao

Abstract

In this article, we study a class of semiparametric mixtures of regression models, in which the regression functions are linear functions of the predictors, but the mixing proportions are smoothing functions of a covariate. We propose a one-step backfitting estimation procedure to achieve the optimal convergence rates for both regression parameters and the nonparametric functions of mixing proportions. We derive the asymptotic bias and variance of the one-step estimate, and further establish its asymptotic normality. A modified expectation-maximization-type (EM-type) estimation procedure is investigated. We show that the modified EM algorithms preserve the asymptotic ascent property. Numerical simulations are conducted to examine the finite sample performance of the estimation procedures. The proposed methodology is further illustrated via an analysis of a real dataset.

Suggested Citation

  • 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.
  • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:711-724
    DOI: 10.1080/01621459.2012.682541
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    File URL: http://hdl.handle.net/10.1080/01621459.2012.682541
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    Citations

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    Cited by:

    1. Tran, Kien C. & Tsionas, Mike G., 2016. "Zero-inefficiency stochastic frontier models with varying mixing proportion: A semiparametric approach," European Journal of Operational Research, Elsevier, vol. 249(3), pages 1113-1123.
    2. Lu, Xiaosun & Huang, Yangxin & Zhu, Yiliang, 2016. "Finite mixture of nonlinear mixed-effects joint models in the presence of missing and mismeasured covariate, with application to AIDS studies," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 119-130.
    3. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.
    4. 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.
    5. repec:spr:aistmt:v:70:y:2018:i:1:d:10.1007_s10463-016-0584-7 is not listed on IDEAS
    6. Yuzhu Tian & Manlai Tang & Maozai Tian, 2016. "A class of finite mixture of quantile regressions with its applications," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(7), pages 1240-1252, July.
    7. 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.

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