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Estimating Mixture of Gaussian Processes by Kernel Smoothing

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  • Mian Huang
  • Runze Li
  • Hansheng Wang
  • Weixin Yao

Abstract

When functional data are not homogenous, for example, when there are multiple classes of functional curves in the dataset, traditional estimation methods may fail. In this article, we propose a new estimation procedure for the mixture of Gaussian processes, to incorporate both functional and inhomogenous properties of the data. Our method can be viewed as a natural extension of high-dimensional normal mixtures. However, the key difference is that smoothed structures are imposed for both the mean and covariance functions. The model is shown to be identifiable, and can be estimated efficiently by a combination of the ideas from expectation-maximization (EM) algorithm, kernel regression, and functional principal component analysis. Our methodology is empirically justified by Monte Carlo simulations and illustrated by an analysis of a supermarket dataset.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:jnlbes:v:32:y:2014:i:2:p:259-270
    DOI: 10.1080/07350015.2013.868084
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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. Lueken, Roger & Apt, Jay & Sowell, Fallaw, 2016. "Robust resource adequacy planning in the face of coal retirements," Energy Policy, Elsevier, vol. 88(C), pages 371-388.

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