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Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression

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  • Wang, Shangshan
  • Xiang, Liming

Abstract

We advocate linear regression by modeling the error term through a finite mixture of asymmetric Laplace distributions (ALDs). The model expands the flexibility of linear regression to account for heterogeneity among data and allows us to establish the equivalence between maximum likelihood estimation of the model parameters and the composite quantile regression (CQR) estimation developed by Zou and Yuan (Ann. Stat. 36:1108–1126, 2008), providing a new likelihood-based solution to CQR. Particularly, we develop a computationally efficient estimation procedure via a two-layer EM algorithm, where the first layer EM algorithm incorporates missing information from the component memberships of the mixture model and nests the second layer EM in its M-step to accommodate latent variables involved in the location-scale mixture representation of the ALD. An appealing feature of the proposed algorithm is that the closed form updates for parameters in each iteration are obtained explicitly, instead of resorting to numerical optimization methods as in the existing work. Computational complexity can be reduced significantly. We evaluate the performance through simulation studies and illustrate its usefulness by analyzing a gene expression dataset.

Suggested Citation

  • Wang, Shangshan & Xiang, Liming, 2017. "Two-layer EM algorithm for ALD mixture regression models: A new solution to composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 136-154.
    • Handle: RePEc:eee:csdana:v:115:y:2017:i:c:p:136-154
    DOI: 10.1016/j.csda.2017.06.002
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    References listed on IDEAS

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    Cited by:

    1. Shanshan Wang & Tianhao Zhao & Haitao Zheng & Jie Hu, 2017. "The STIRPAT Analysis on Carbon Emission in Chinese Cities: An Asymmetric Laplace Distribution Mixture Model," Sustainability, MDPI, vol. 9(12), pages 1-13, December.
    2. Xiaohui Yuan & Yong Li & Xiaogang Dong & Tianqing Liu, 2022. "Optimal subsampling for composite quantile regression in big data," Statistical Papers, Springer, vol. 63(5), pages 1649-1676, October.
    3. Huiwen Wang & Ruiping Liu & Shanshan Wang & Zhichao Wang & Gilbert Saporta, 2020. "Ultra-high dimensional variable screening via Gram–Schmidt orthogonalization," Computational Statistics, Springer, vol. 35(3), pages 1153-1170, September.

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