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A Gaussian process regression approach to a single-index model

Author

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  • Taeryon Choi
  • Jian Shi
  • Bo Wang

Abstract

We consider a Gaussian process regression (GPR) approach to analysing a single-index model (SIM) from the Bayesian perspective. Specifically, the unknown link function is assumed to be a Gaussian process a priori and a prior on the index vector is considered based on a simple uniform distribution on the unit sphere. The posterior distributions for the unknown parameters are derived, and the posterior inference of the proposed approach is performed via Markov chain Monte Carlo methods based on them. Particularly, in estimating the hyperparameters, different numerical schemes are implemented: fully Bayesian methods and empirical Bayes methods. Numerical illustration of the proposed approach is also made using simulation data as well as well-known real data. The proposed approach broadens the scope of the applicability of the SIM as well as the GPR. In addition, we discuss the theoretical aspect of the proposed method in terms of posterior consistency.

Suggested Citation

  • Taeryon Choi & Jian Shi & Bo Wang, 2011. "A Gaussian process regression approach to a single-index model," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 23(1), pages 21-36.
    • Handle: RePEc:taf:gnstxx:v:23:y:2011:i:1:p:21-36
    DOI: 10.1080/10485251003768019
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    Cited by:

    1. Wai-Yin Poon & Hai-Bin Wang, 2014. "Multivariate partially linear single-index models: Bayesian analysis," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(4), pages 755-768, December.
    2. Glen McGee & Ander Wilson & Thomas F. Webster & Brent A. Coull, 2023. "Bayesian multiple index models for environmental mixtures," Biometrics, The International Biometric Society, vol. 79(1), pages 462-474, March.
    3. Hyung G. Park & Danni Wu & Eva Petkova & Thaddeus Tarpey & R. Todd Ogden, 2023. "Bayesian Index Models for Heterogeneous Treatment Effects on a Binary Outcome," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(2), pages 397-418, July.
    4. Taha Alshaybawee & Habshah Midi & Rahim Alhamzawi, 2017. "Bayesian elastic net single index quantile regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(5), pages 853-871, April.
    5. Levi, Evgeny & Craiu, Radu V., 2018. "Bayesian inference for conditional copulas using Gaussian Process single index models," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 115-134.

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