IDEAS home Printed from https://ideas.repec.org/a/spr/stabio/v16y2024i1d10.1007_s12561-023-09393-7.html
   My bibliography  Save this article

On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model

Author

Listed:
  • Haiyan Liu

    (University of Leeds)

  • Georgios Aivaliotis

    (University of Leeds)

  • Vijay Kumar

    (University of Sussex)

  • Jeanine Houwing-Duistermaat

    (University of Leeds
    Radboud University Nijmegen)

Abstract

We propose a functional linear model to predict a functional response using multiple functional and longitudinal predictors and to estimate the effect lags of predictors. The coefficient functions are written as the expansion of a basis system (e.g. functional principal components, splines), and the coefficients of the basis functions are estimated via optimizing a penalization criterion. Then effect lags are determined by simultaneously searching on a prior designed grid mesh based on minimization of a proposed prediction error criterion. Mathematical properties of the estimated regression functions and predicted responses are studied. The performance of the method is evaluated by extensive simulations and a real data analysis application on chronic obstructive pulmonary disease (COPD).

Suggested Citation

  • Haiyan Liu & Georgios Aivaliotis & Vijay Kumar & Jeanine Houwing-Duistermaat, 2024. "On Estimation of the Effect Lag of Predictors and Prediction in a Functional Linear Model," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 16(1), pages 1-24, April.
    • Handle: RePEc:spr:stabio:v:16:y:2024:i:1:d:10.1007_s12561-023-09393-7
    DOI: 10.1007/s12561-023-09393-7
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s12561-023-09393-7
    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/s12561-023-09393-7?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. 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. Yao, Fang & Muller, Hans-Georg & Wang, Jane-Ling, 2005. "Functional Data Analysis for Sparse Longitudinal Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 577-590, June.
    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. 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.
    2. Ana-Maria Staicu & Yingxing Li & Ciprian M. Crainiceanu & David Ruppert, 2014. "Likelihood Ratio Tests for Dependent Data with Applications to Longitudinal and Functional Data Analysis," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 41(4), pages 932-949, December.
    3. Şentürk, Damla & Ghosh, Samiran & Nguyen, Danh V., 2014. "Exploratory time varying lagged regression: Modeling association of cognitive and functional trajectories with expected clinic visits in older adults," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 1-15.
    4. Álvarez-Liébana, J. & López-Pérez, A. & González-Manteiga, W. & Febrero-Bande, M., 2025. "A goodness-of-fit test for functional time series with applications to Ornstein-Uhlenbeck processes," Computational Statistics & Data Analysis, Elsevier, vol. 203(C).
    5. Wang, Jingxing & Chung, Seokhyun & AlShelahi, Abdullah & Kontar, Raed & Byon, Eunshin & Saigal, Romesh, 2021. "Look-ahead decision making for renewable energy: A dynamic “predict and store” approach," Applied Energy, Elsevier, vol. 296(C).
    6. Heredia, María Belén & Prieur, Clémentine & Eckert, Nicolas, 2022. "Global sensitivity analysis with aggregated Shapley effects, application to avalanche hazard assessment," Reliability Engineering and System Safety, Elsevier, vol. 222(C).
    7. Febrero-Bande, Manuel & González-Manteiga, Wenceslao & Prallon, Brenda & Saporito, Yuri F., 2023. "Functional classification of bitcoin addresses," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    8. Li, Pai-Ling & Chiou, Jeng-Min, 2011. "Identifying cluster number for subspace projected functional data clustering," Computational Statistics & Data Analysis, Elsevier, vol. 55(6), pages 2090-2103, June.
    9. Shuyu Meng & Zhensheng Huang, 2024. "Variable Selection in Semi-Functional Partially Linear Regression Models with Time Series Data," Mathematics, MDPI, vol. 12(17), pages 1-23, September.
    10. Xiuli Du & Xiaohu Jiang & Jinguan Lin, 2023. "Multinomial Logistic Factor Regression for Multi-source Functional Block-wise Missing Data," Psychometrika, Springer;The Psychometric Society, vol. 88(3), pages 975-1001, September.
    11. Guangxing Wang & Sisheng Liu & Fang Han & Chong‐Zhi Di, 2023. "Robust functional principal component analysis via a functional pairwise spatial sign operator," Biometrics, The International Biometric Society, vol. 79(2), pages 1239-1253, June.
    12. Jiménez Recaredo, Raúl José & Elías Fernández, Antonio, 2017. "Prediction Bands for Functional Data Based on Depth Measures," DES - Working Papers. Statistics and Econometrics. WS 24606, Universidad Carlos III de Madrid. Departamento de Estadística.
    13. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    14. Li, Pai-Ling & Chiou, Jeng-Min & Shyr, Yu, 2017. "Functional data classification using covariate-adjusted subspace projection," Computational Statistics & Data Analysis, Elsevier, vol. 115(C), pages 21-34.
    15. Xiongtao Dai & Zhenhua Lin & Hans‐Georg Müller, 2021. "Modeling sparse longitudinal data on Riemannian manifolds," Biometrics, The International Biometric Society, vol. 77(4), pages 1328-1341, December.
    16. Poskitt, D.S. & Sengarapillai, Arivalzahan, 2013. "Description length and dimensionality reduction in functional data analysis," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 98-113.
    17. Park, So Young & Xiao, Luo & Willbur, Jayson D. & Staicu, Ana-Maria & Jumbe, N. L’ntshotsholé, 2018. "A joint design for functional data with application to scheduling ultrasound scans," Computational Statistics & Data Analysis, Elsevier, vol. 122(C), pages 101-114.
    18. Mingfei Dong & Donatello Telesca & Catherine Sugar & Frederick Shic & Adam Naples & Scott P. Johnson & Beibin Li & Adham Atyabi & Minhang Xie & Sara J. Webb & Shafali Jeste & Susan Faja & April R. Lev, 2023. "A Functional Model for Studying Common Trends Across Trial Time in Eye Tracking Experiments," Statistics in Biosciences, Springer;International Chinese Statistical Association, vol. 15(1), pages 261-287, April.
    19. González-Rodríguez, Gil & Colubi, Ana, 2017. "On the consistency of bootstrap methods in separable Hilbert spaces," Econometrics and Statistics, Elsevier, vol. 1(C), pages 118-127.
    20. Hao Zhang, 2016. "Comments on: Probability enhanced effective dimension reduction for classifying sparse functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(1), pages 47-51, March.

    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:stabio:v:16:y:2024:i:1:d:10.1007_s12561-023-09393-7. 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.