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Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition

Author

Listed:
  • Yuzhu Tian

    (Henan University of Science and Technology)

  • Hongmei Lin

    (Shanghai University of International Business and Economics)

  • Heng Lian

    (City University of Hong Kong)

  • Zengyan Fan

    (Singapore University of Social Sciences)

Abstract

Additive functional model is one popular semiparametric approach for regression with a functional predictor. Optimal prediction error rate has been demonstrated in the framework of reproducing kernel Hilbert spaces (RKHS), which only depends on the property of the RKHS but not on the smoothness of the function. We extend this previous theoretical result by establishing faster convergence rates under stronger conditions which is reduced to existing results when the stronger condition is removed. In particular, our result shows that with a smoother function the convergence rate of the estimator is faster.

Suggested Citation

  • Yuzhu Tian & Hongmei Lin & Heng Lian & Zengyan Fan, 2021. "Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(3), pages 429-442, April.
    • Handle: RePEc:spr:metrik:v:84:y:2021:i:3:d:10.1007_s00184-020-00797-9
    DOI: 10.1007/s00184-020-00797-9
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    References listed on IDEAS

    as
    1. Müller, Hans-Georg & Yao, Fang, 2008. "Functional Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 103(484), pages 1534-1544.
    2. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
    3. Hongxiao Zhu & Fang Yao & Hao Helen Zhang, 2014. "Structured functional additive regression in reproducing kernel Hilbert spaces," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(3), pages 581-603, June.
    4. Hans-Georg Müller & Yichao Wu & Fang Yao, 2013. "Continuously additive models for nonlinear functional regression," Biometrika, Biometrika Trust, vol. 100(3), pages 607-622.
    Full references (including those not matched with items on IDEAS)

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