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Machine Learning Embedded Semiparametric Mixtures of Regressions with Covariate-Varying Mixing Proportions

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  • Xue, Jiacheng
  • Yao, Weixin

Abstract

A new class of semiparametric mixture regression models with covariate-varying mixing proportions is introduced by embedding machine learning methods into mixtures of regressions. The new method uses the neural network to estimate mixing proportions nonparametrically while using the maximum likelihood estimate to estimate all other component parameters. The new machine learning embedded semiparametric mixture regression models offer more flexible estimation compared to traditional parametric mixture regression models. More importantly, the new hybrid method could better estimate the effects of multivariate covariates nonparametrically than the traditional kernel regression methods, which suffer from the well known “curse of dimensionality”. The introduced hybrid idea can be easily extended to other semiparametric statistical models and other machine learning methods. Simulation studies and a real data application are used to demonstrate the effectiveness of the proposed new method and compare it with some other existing methods.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ecosta:v:22:y:2022:i:c:p:159-171
    DOI: 10.1016/j.ecosta.2021.10.018
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    1. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    2. Goldfeld, Stephen M. & Quandt, Richard E., 1973. "A Markov model for switching regressions," Journal of Econometrics, Elsevier, vol. 1(1), pages 3-15, March.
    3. Benaglia, Tatiana & Chauveau, Didier & Hunter, David R. & Young, Derek S., 2009. "mixtools: An R Package for Analyzing Mixture Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 32(i06).
    4. Young, D.S. & Hunter, D.R., 2010. "Mixtures of regressions with predictor-dependent mixing proportions," Computational Statistics & Data Analysis, Elsevier, vol. 54(10), pages 2253-2266, October.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. Matthew Stephens, 2000. "Dealing with label switching in mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(4), pages 795-809.
    10. 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.
    11. 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.
    12. 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.
    13. Mirfarah, Elham & Naderi, Mehrdad & Chen, Ding-Geng, 2021. "Mixture of linear experts model for censored data: A novel approach with scale-mixture of normal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 158(C).
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