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Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition

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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.

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Acknowledgements

We sincerely thank Editor-in-Chief Professor Maria Kateri, the Associate Editor, and two anonymous reviewers for their insightful comments that greatly improved the manuscript.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Henan University of Science and Technology, LuoYang, China

    Yuzhu Tian

  2. School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai, China

    Hongmei Lin

  3. Department of Mathematics, City University of Hong Kong, Hong Kong, China

    Heng Lian

  4. School of Science and Technology, Singapore University of Social Sciences, Singapore, Singapore

    Zengyan Fan

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  1. Yuzhu Tian
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  2. Hongmei Lin
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  3. Heng Lian
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  4. Zengyan Fan
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Correspondence to Hongmei Lin.

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Tian, Y., Lin, H., Lian, H. et al. Additive functional regression in reproducing kernel Hilbert spaces under smoothness condition. Metrika 84, 429–442 (2021). https://doi.org/10.1007/s00184-020-00797-9

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  • DOI: https://doi.org/10.1007/s00184-020-00797-9

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