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Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule

Author

Listed:
  • Jia Chen

    (School of Mathematics, Sichuan University of Arts and Science, Dazhou 635000, China)

  • Junke Kou

    (School of Mathematics and Computational Science, Guilin University of Electronic Technology, Guilin 541004, China)

Abstract

For nonparametric regression estimation, conventional research all focus on isotropic regression function. In this paper, a linear wavelet estimator of anisotropic regression function is constructed, the rate of convergence of this estimator is discussed in anisotropic Besov spaces. More importantly, in order to obtain an adaptive estimator, a regression estimator is proposed with scaling parameter data-driven selection rule. It turns out that our results attain the optimal convergence rate of nonparametric pointwise estimation.

Suggested Citation

  • Jia Chen & Junke Kou, 2023. "Pointwise Estimation of Anisotropic Regression Functions Using Wavelets with Data-Driven Selection Rule," Mathematics, MDPI, vol. 12(1), pages 1-10, December.
    • Handle: RePEc:gam:jmathe:v:12:y:2023:i:1:p:98-:d:1308723
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    References listed on IDEAS

    as
    1. Huijun Guo & Junke Kou, 2019. "Non linear wavelet estimation of regression derivatives based on biased data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 48(13), pages 3219-3235, July.
    2. Kou, Junke & Liu, Youming, 2016. "An extension of Chesneau’s theorem," Statistics & Probability Letters, Elsevier, vol. 108(C), pages 23-32.
    3. Junke Kou & Youming Liu, 2017. "Non parametric regression estimations over Lp risk based on biased data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 46(5), pages 2375-2395, March.
    4. Christophe Chesneau & Esmaeil Shirazi, 2014. "Nonparametric Wavelet Regression Based on Biased Data," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 43(13), pages 2642-2658, July.
    Full references (including those not matched with items on IDEAS)

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