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Fast rates of exponential cost function

Author

Listed:
  • Qian Sun

    (Hubei Normal University)

  • Yang Zhou

    (Beijing Normal University)

  • Shouyou Huang

    (Hubei Normal University)

Abstract

In this paper, we introduce a new algorithm of learning with exponential cost function within the framework of statistical learning theory. We establish an important comparison theorem that illustrates the relationship between the prediction error and the excess generalization error under the moment condition. Furthermore, the paper investigates the generalization performance of algorithm and the robustness of exponential cost function. We prove that the resulting estimator enjoys asymptotic optimality and robustness under certain conditions. Numerical simulations are provided to demonstrate our theoretical findings.

Suggested Citation

  • Qian Sun & Yang Zhou & Shouyou Huang, 2025. "Fast rates of exponential cost function," Statistical Papers, Springer, vol. 66(3), pages 1-19, April.
    • Handle: RePEc:spr:stpapr:v:66:y:2025:i:3:d:10.1007_s00362-025-01672-3
    DOI: 10.1007/s00362-025-01672-3
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    References listed on IDEAS

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    1. Hu Yang & Ning Li & Jing Yang, 2020. "A robust and efficient estimation and variable selection method for partially linear models with large-dimensional covariates," Statistical Papers, Springer, vol. 61(5), pages 1911-1937, October.
    2. Liugen Xue & Junshan Xie, 2024. "Efficient robust estimation for single-index mixed effects models with missing observations," Statistical Papers, Springer, vol. 65(2), pages 827-864, April.
    3. Xueqin Wang & Yunlu Jiang & Mian Huang & Heping Zhang, 2013. "Robust Variable Selection With Exponential Squared Loss," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(502), pages 632-643, June.
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