IDEAS home Printed from https://ideas.repec.org/a/spr/metrik/v84y2021i3d10.1007_s00184-020-00797-9.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00184-020-00797-9
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00184-020-00797-9?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    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)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kehui Chen & Xiaoke Zhang & Alexander Petersen & Hans-Georg Müller, 2017. "Quantifying Infinite-Dimensional Data: Functional Data Analysis in Action," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 9(2), pages 582-604, December.
    2. Shang, Han Lin, 2013. "Bayesian bandwidth estimation for a nonparametric functional regression model with unknown error density," Computational Statistics & Data Analysis, Elsevier, vol. 67(C), pages 185-198.
    3. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    4. Liu, Yuzi & Peng, Ling & Liu, Qing & Lian, Heng & Liu, Xiaohui, 2023. "Functional additive expectile regression in the reproducing kernel Hilbert space," Journal of Multivariate Analysis, Elsevier, vol. 198(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.
    6. Philip T. Reiss & Jeff Goldsmith & Han Lin Shang & R. Todd Ogden, 2017. "Methods for Scalar-on-Function Regression," International Statistical Review, International Statistical Institute, vol. 85(2), pages 228-249, August.
    7. Wang, Bo & Xu, Aiping, 2019. "Gaussian process methods for nonparametric functional regression with mixed predictors," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 80-90.
    8. Sang, Peijun & Lockhart, Richard A. & Cao, Jiguo, 2018. "Sparse estimation for functional semiparametric additive models," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 105-118.
    9. Liu, Yanghui & Li, Yehua & Carroll, Raymond J. & Wang, Naisyin, 2022. "Predictive functional linear models with diverging number of semiparametric single-index interactions," Journal of Econometrics, Elsevier, vol. 230(2), pages 221-239.
    10. F. Ferraty & A. Goia & E. Salinelli & P. Vieu, 2013. "Functional projection pursuit regression," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(2), pages 293-320, June.
    11. Zhu, Hanbing & Li, Rui & Zhang, Riquan & Lian, Heng, 2020. "Nonlinear functional canonical correlation analysis via distance covariance," Journal of Multivariate Analysis, Elsevier, vol. 180(C).
    12. Yang, Yang & Yang, Yanrong & Shang, Han Lin, 2022. "Feature extraction for functional time series: Theory and application to NIR spectroscopy data," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    13. Ufuk Beyaztas & Han Lin Shang, 2021. "A partial least squares approach for function-on-function interaction regression," Computational Statistics, Springer, vol. 36(2), pages 911-939, June.
    14. G. Aneiros & P. Vieu, 2016. "Sparse nonparametric model for regression with functional covariate," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 28(4), pages 839-859, October.
    15. Huang, Lele & Zhao, Junlong & Wang, Huiwen & Wang, Siyang, 2016. "Robust shrinkage estimation and selection for functional multiple linear model through LAD loss," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 384-400.
    16. Bergsma, Wicher P, 2020. "Regression with I-priors," Econometrics and Statistics, Elsevier, vol. 14(C), pages 89-111.
    17. Klaus Ackermann & Simon D Angus & Paul A Raschky, 2020. "Estimating Sleep and Work Hours from Alternative Data by Segmented Functional Classification Analysis, SFCA," SoDa Laboratories Working Paper Series 2020-04, Monash University, SoDa Laboratories.
    18. C. Abraham & G. Biau & B. Cadre, 2006. "On the Kernel Rule for Function Classification," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(3), pages 619-633, September.
    19. Delsol, Laurent & Ferraty, Frédéric & Vieu, Philippe, 2011. "Structural test in regression on functional variables," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 422-447, March.
    20. Nengxiang Ling & Rui Kan & Philippe Vieu & Shuyu Meng, 2019. "Semi-functional partially linear regression model with responses missing at random," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(1), pages 39-70, January.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:metrik:v:84:y:2021:i:3:d:10.1007_s00184-020-00797-9. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.