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A general robust t-process regression model

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  • Wang, Zhanfeng
  • Noh, Maengseok
  • Lee, Youngjo
  • Shi, Jian Qing

Abstract

The Gaussian process regression (GPR) model is well-known to be susceptible to outliers. Robust process regression models based on t-process or other heavy-tailed processes have been developed to address the problem. However, due to the current definitions of heavy-tailed processes, the unknown process regression function and the random errors are always defined jointly. This definition, mainly owing to mix-up of the regression function modeling and the distribution of the random errors, is not justified in many practical problems and thus limits the application of those robust approaches. It also results in a limitation of the statistical properties and robust analysis. A general robust process regression model is proposed by separating the nonparametric regression model from the distribution assumption of the random error. An efficient estimation procedure is developed. It shows that the estimated random-effects are useful in detecting outlying curves. Statistical properties, such as unbiasedness and information consistency, are provided. Numerical studies show that the proposed method is robust against outliers and outlying curves, and has a better performance in prediction compared with the existing models.

Suggested Citation

  • Wang, Zhanfeng & Noh, Maengseok & Lee, Youngjo & Shi, Jian Qing, 2021. "A general robust t-process regression model," Computational Statistics & Data Analysis, Elsevier, vol. 154(C).
    • Handle: RePEc:eee:csdana:v:154:y:2021:i:c:s0167947320301845
    DOI: 10.1016/j.csda.2020.107093
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    References listed on IDEAS

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    1. Bo Wang & Jian Qing Shi, 2014. "Generalized Gaussian Process Regression Model for Non-Gaussian Functional Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1123-1133, September.
    2. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    3. Lee Youngjo & Gwangsu Kim, 2020. "Properties of h‐Likelihood Estimators in Clustered Data," International Statistical Review, International Statistical Institute, vol. 88(2), pages 380-395, August.
    4. Choi, Taeryon & Schervish, Mark J., 2007. "On posterior consistency in nonparametric regression problems," Journal of Multivariate Analysis, Elsevier, vol. 98(10), pages 1969-1987, November.
    5. J. Q. Shi & B. Wang & R. Murray-Smith & D. M. Titterington, 2007. "Gaussian Process Functional Regression Modeling for Batch Data," Biometrics, The International Biometric Society, vol. 63(3), pages 714-723, September.
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