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Laplace mixture of linear experts

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  • Nguyen, Hien D.
  • McLachlan, Geoffrey J.

Abstract

Mixture of Linear Experts (MoLE) models provide a popular framework for modeling nonlinear regression data. The majority of applications of MoLE models utilizes a Gaussian distribution for regression error. Such assumptions are known to be sensitive to outliers. The use of a Laplace distributed error is investigated. This model is named the Laplace MoLE (LMoLE). Links are drawn between the Laplace error model and the least absolute deviations regression criterion, which is known to be robust among a wide class of criteria. Through application of the minorization–maximization algorithm framework, an algorithm is derived that monotonically increases the likelihood in the estimation of the LMoLE model parameters. It is proven that the maximum likelihood estimator (MLE) for the parameter vector of the LMoLE is consistent. Through simulation studies, the robustness of the LMoLE model over the Gaussian MOLE model is demonstrated, and support for the consistency of the MLE is provided. An application of the LMoLE model to the analysis of a climate science data set is described.

Suggested Citation

  • Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Laplace mixture of linear experts," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 177-191.
    • Handle: RePEc:eee:csdana:v:93:y:2016:i:c:p:177-191
    DOI: 10.1016/j.csda.2014.10.016
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    Cited by:

    1. Hien Duy Nguyen & TrungTin Nguyen & Faicel Chamroukhi & Geoffrey John McLachlan, 2021. "Approximations of conditional probability density functions in Lebesgue spaces via mixture of experts models," Journal of Statistical Distributions and Applications, Springer, vol. 8(1), pages 1-15, December.
    2. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Linear mixed models with marginally symmetric nonparametric random effects," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 151-169.
    3. Sugasawa, Shonosuke & Kobayashi, Genya, 2022. "Robust fitting of mixture models using weighted complete estimating equations," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    4. Nguyen, Hien D. & McLachlan, Geoffrey J. & Ullmann, Jeremy F.P. & Janke, Andrew L., 2016. "Laplace mixture autoregressive models," Statistics & Probability Letters, Elsevier, vol. 110(C), pages 18-24.
    5. Lloyd-Jones, Luke R. & Nguyen, Hien D. & McLachlan, Geoffrey J., 2018. "A globally convergent algorithm for lasso-penalized mixture of linear regression models," Computational Statistics & Data Analysis, Elsevier, vol. 119(C), pages 19-38.
    6. Kang-Ping Lu & Shao-Tung Chang, 2022. "Robust Switching Regressions Using the Laplace Distribution," Mathematics, MDPI, vol. 10(24), pages 1-24, December.
    7. Nguyen, Hien D. & McLachlan, Geoffrey J., 2016. "Maximum likelihood estimation of triangular and polygonal distributions," Computational Statistics & Data Analysis, Elsevier, vol. 102(C), pages 23-36.
    8. 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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