IDEAS home Printed from https://ideas.repec.org/a/bla/biomet/v78y2022i3p1031-1044.html
   My bibliography  Save this article

Restricted function‐on‐function linear regression model

Author

Listed:
  • Ruiyan Luo
  • Xin Qi

Abstract

The usual function‐on‐function linear regression model depicts the association between functional variables in the whole rectangular region and the value of response curve at any point is influenced by the entire trajectory of the predictor curve. But in addition to this, there are cases where the value of the response curve at a point is only influenced by the value of the predictor curve in a subregion, such as the historical relationship and the short‐term association. We will consider the restricted function‐on‐function regression model, where the value of response curve at any point is influenced by a subtrajectory of the predictor. We have two major purposes. First, we propose a novel estimation procedure that is more accurate and computational efficient for the restricted function‐on‐function model with a given subregion. Second, as the subregion is seldom specified in practice, we propose a subregion selection procedure that can lead to models with better interpretation and predictive performance. Algorithms are developed for both model estimation and subregion selection.

Suggested Citation

  • Ruiyan Luo & Xin Qi, 2022. "Restricted function‐on‐function linear regression model," Biometrics, The International Biometric Society, vol. 78(3), pages 1031-1044, September.
    • Handle: RePEc:bla:biomet:v:78:y:2022:i:3:p:1031-1044
    DOI: 10.1111/biom.13463
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/biom.13463
    Download Restriction: no
    File URL: https://libkey.io/10.1111/biom.13463?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
    ---><---

    References listed on IDEAS

    as
    1. Harezlak, Jaroslaw & Coull, Brent A. & Laird, Nan M. & Magari, Shannon R. & Christiani, David C., 2007. "Penalized solutions to functional regression problems," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4911-4925, June.
    2. Ruiyan Luo & Xin Qi, 2017. "Function-on-Function Linear Regression by Signal Compression," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(518), pages 690-705, April.
    3. Xiaoxiao Sun & Pang Du & Xiao Wang & Ping Ma, 2018. "Optimal Penalized Function-on-Function Regression Under a Reproducing Kernel Hilbert Space Framework," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 113(524), pages 1601-1611, October.
    4. Shuang Wu & Hans-Georg Müller, 2011. "Response-Adaptive Regression for Longitudinal Data," Biometrics, The International Biometric Society, vol. 67(3), pages 852-860, September.
    5. Chiou, Jeng-Min & Yang, Ya-Fang & Chen, Yu-Ting, 2016. "Multivariate functional linear regression and prediction," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 301-312.
    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. Zhou, Zhiyang, 2021. "Fast implementation of partial least squares for function-on-function regression," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    2. Qi, Xin & Luo, Ruiyan, 2018. "Function-on-function regression with thousands of predictive curves," Journal of Multivariate Analysis, Elsevier, vol. 163(C), pages 51-66.
    3. 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.
    4. Łukasz Smaga & Hidetoshi Matsui, 2018. "A note on variable selection in functional regression via random subspace method," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(3), pages 455-477, August.
    5. Centofanti, Fabio & Fontana, Matteo & Lepore, Antonio & Vantini, Simone, 2022. "Smooth LASSO estimator for the Function-on-Function linear regression model," Computational Statistics & Data Analysis, Elsevier, vol. 176(C).
    6. Chen, Haitao & Zhang, Bin & Liu, Hua & Cao, Jiguo, 2024. "The inequality in household electricity consumption due to temperature change: Data driven analysis with a function-on-function linear model," Energy, Elsevier, vol. 288(C).
    7. Fabio Centofanti & Antonio Lepore & Alessandra Menafoglio & Biagio Palumbo & Simone Vantini, 2023. "Adaptive smoothing spline estimator for the function-on-function linear regression model," Computational Statistics, Springer, vol. 38(1), pages 191-216, March.
    8. Shuzhi Zhu & Peixin Zhao, 2019. "Tests for the linear hypothesis in semi-functional partial linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 82(2), pages 125-148, March.
    9. Martínez-Hernández, Israel & Genton, Marc G. & González-Farías, Graciela, 2019. "Robust depth-based estimation of the functional autoregressive model," Computational Statistics & Data Analysis, Elsevier, vol. 131(C), pages 66-79.
    10. Ruzong Fan & Hong-Bin Fang, 2022. "Stochastic functional linear models and Malliavin calculus," Computational Statistics, Springer, vol. 37(2), pages 591-611, April.
    11. Ajroldi, Niccolò & Diquigiovanni, Jacopo & Fontana, Matteo & Vantini, Simone, 2023. "Conformal prediction bands for two-dimensional functional time series," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    12. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    13. Cody Carroll & Hans‐Georg Müller, 2023. "Latent deformation models for multivariate functional data and time‐warping separability," Biometrics, The International Biometric Society, vol. 79(4), pages 3345-3358, December.
    14. 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.
    15. Chang, Jinyuan & Chen, Cheng & Qiao, Xinghao & Yao, Qiwei, 2023. "An autocovariance-based learning framework for high-dimensional functional time series," LSE Research Online Documents on Economics 117910, London School of Economics and Political Science, LSE Library.
    16. Ali Mahzarnia & Jun Song, 2022. "Multivariate functional group sparse regression: Functional predictor selection," PLOS ONE, Public Library of Science, vol. 17(4), pages 1-22, April.
    17. Vieu, Philippe, 2018. "On dimension reduction models for functional data," Statistics & Probability Letters, Elsevier, vol. 136(C), pages 134-138.
    18. Aneiros, Germán & Horová, Ivana & Hušková, Marie & Vieu, Philippe, 2022. "On functional data analysis and related topics," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    19. Han Shang, 2014. "A survey of functional principal component analysis," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(2), pages 121-142, April.
    20. Cui, Xia & Lin, Hongmei & Lian, Heng, 2020. "Partially functional linear regression in reproducing kernel Hilbert spaces," Computational Statistics & Data Analysis, Elsevier, vol. 150(C).

    More about this item

    Statistics

    Access and download statistics

    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:bla:biomet:v:78:y:2022:i:3:p:1031-1044. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0006-341X .

    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.