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Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces

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  • Lian, Heng

Abstract

In this article, we consider convergence rates in functional linear regression with functional responses, where the linear coefficient lies in a reproducing kernel Hilbert space (RKHS). Without assuming that the reproducing kernel and the covariate covariance kernel are aligned, convergence rates in prediction risk are established. The corresponding lower bound in rates is derived by reducing to the scalar response case. Simulation studies and two benchmark datasets are used to illustrate that the proposed approach can significantly outperform the functional PCA approach in prediction.

Suggested Citation

  • Lian, Heng, 2015. "Minimax prediction for functional linear regression with functional responses in reproducing kernel Hilbert spaces," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 395-402.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:395-402
    DOI: 10.1016/j.jmva.2015.06.005
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    References listed on IDEAS

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    1. Frédéric Ferraty & Philippe Vieu, 2002. "The Functional Nonparametric Model and Application to Spectrometric Data," Computational Statistics, Springer, vol. 17(4), pages 545-564, December.
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    Cited by:

    1. Zhou, Zhiyang, 2021. "Fast implementation of partial least squares for function-on-function regression," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Imaizumi, Masaaki & Kato, Kengo, 2018. "PCA-based estimation for functional linear regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 15-36.
    3. Wang, Lei & Zhang, Jing & Li, Bo & Liu, Xiaohui, 2022. "Quantile trace regression via nuclear norm regularization," Statistics & Probability Letters, Elsevier, vol. 182(C).
    4. Cui, Xia & Lin, Hongmei & Lian, Heng, 2020. "Partially functional linear regression in reproducing kernel Hilbert spaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).
    5. Lin, Hongmei & Jiang, Xuejun & Lian, Heng & Zhang, Weiping, 2019. "Reduced rank modeling for functional regression with functional responses," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 205-217.

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