IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v38y2023i1d10.1007_s00180-022-01223-6.html
   My bibliography  Save this article

Adaptive smoothing spline estimator for the function-on-function linear regression model

Author

Listed:
  • Fabio Centofanti

    (University of Naples Federico II)

  • Antonio Lepore

    (University of Naples Federico II)

  • Alessandra Menafoglio

    (MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano)

  • Biagio Palumbo

    (University of Naples Federico II)

  • Simone Vantini

    (MOX - Modelling and Scientific Computing, Department of Mathematics, Politecnico di Milano)

Abstract

In this paper, we propose an adaptive smoothing spline (AdaSS) estimator for the function-on-function linear regression model where each value of the response, at any domain point, depends on the full trajectory of the predictor. The AdaSS estimator is obtained by the optimization of an objective function with two spatially adaptive penalties, based on initial estimates of the partial derivatives of the regression coefficient function. This allows the proposed estimator to adapt more easily to the true coefficient function over regions of large curvature and not to be undersmoothed over the remaining part of the domain. A novel evolutionary algorithm is developed ad hoc to obtain the optimization tuning parameters. Extensive Monte Carlo simulations have been carried out to compare the AdaSS estimator with competitors that have already appeared in the literature before. The results show that our proposal mostly outperforms the competitor in terms of estimation and prediction accuracy. Lastly, those advantages are illustrated also in two real-data benchmark examples. The AdaSS estimator is implemented in the R package adass, openly available online on CRAN.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01223-6
    DOI: 10.1007/s00180-022-01223-6
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-022-01223-6
    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/s00180-022-01223-6?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. Alexandre Pintore & Paul Speckman & Chris C. Holmes, 2006. "Spatially adaptive smoothing splines," Biometrika, Biometrika Trust, vol. 93(1), pages 113-125, March.
    2. Canale, Antonio & Vantini, Simone, 2016. "Constrained functional time series: Applications to the Italian gas market," International Journal of Forecasting, Elsevier, vol. 32(4), pages 1340-1351.
    3. Fang Yao & Hans-Georg Müller, 2010. "Functional quadratic regression," Biometrika, Biometrika Trust, vol. 97(1), pages 49-64.
    4. 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.
    5. Gareth M. James, 2002. "Generalized linear models with functional predictors," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 64(3), pages 411-432, August.
    6. Andrada Ivanescu & Ana-Maria Staicu & Fabian Scheipl & Sonja Greven, 2015. "Penalized function-on-function regression," Computational Statistics, Springer, vol. 30(2), pages 539-568, June.
    7. 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.
    8. Cardot, Herve & Crambes, Christophe & Kneip, Alois & Sarda, Pascal, 2007. "Smoothing splines estimators in functional linear regression with errors-in-variables," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4832-4848, June.
    9. 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.
    10. Chiou, Jeng-Min & Müller, Hans-Georg, 2009. "Modeling Hazard Rates as Functional Data for the Analysis of Cohort Lifetables and Mortality Forecasting," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 572-585.
    11. Yang, Lianqiang & Hong, Yongmiao, 2017. "Adaptive penalized splines for data smoothing," Computational Statistics & Data Analysis, Elsevier, vol. 108(C), pages 70-83.
    12. Xiao Wang & Pang Du & Jinglai Shen, 2013. "Smoothing splines with varying smoothing parameter," Biometrika, Biometrika Trust, vol. 100(4), pages 955-970.
    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. 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).
    2. Zhou, Zhiyang, 2021. "Fast implementation of partial least squares for function-on-function regression," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    3. 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.
    4. 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.
    5. Chen, Xuerong & Li, Haoqi & Liang, Hua & Lin, Huazhen, 2019. "Functional response regression analysis," Journal of Multivariate Analysis, Elsevier, vol. 169(C), pages 218-233.
    6. Zhang, Xiaoke & Zhong, Qixian & Wang, Jane-Ling, 2020. "A new approach to varying-coefficient additive models with longitudinal covariates," Computational Statistics & Data Analysis, Elsevier, vol. 145(C).
    7. Hans-Georg Müller & Wenjing Yang, 2010. "Dynamic relations for sparsely sampled Gaussian processes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 19(1), pages 1-29, May.
    8. 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.
    9. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    10. 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.
    11. 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.
    12. Boente, Graciela & Parada, Daniela, 2023. "Robust estimation for functional quadratic regression models," Computational Statistics & Data Analysis, Elsevier, vol. 187(C).
    13. Fang, Xiaolei & Zhou, Rensheng & Gebraeel, Nagi, 2015. "An adaptive functional regression-based prognostic model for applications with missing data," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 266-274.
    14. Chenlin Zhang & Huazhen Lin & Li Liu & Jin Liu & Yi Li, 2023. "Functional data analysis with covariate‐dependent mean and covariance structures," Biometrics, The International Biometric Society, vol. 79(3), pages 2232-2245, September.
    15. Tingting Huang & Gilbert Saporta & Huiwen Wang & Shanshan Wang, 2021. "A robust spatial autoregressive scalar-on-function regression with t-distribution," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(1), pages 57-81, March.
    16. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
    17. Shuang Wu & Hans-Georg Müller, 2011. "Response-Adaptive Regression for Longitudinal Data," Biometrics, The International Biometric Society, vol. 67(3), pages 852-860, September.
    18. Han Lin Shang & Yang Yang, 2021. "Forecasting Australian subnational age-specific mortality rates," Journal of Population Research, Springer, vol. 38(1), pages 1-24, March.
    19. Matsui, Hidetoshi, 2020. "Quadratic regression for functional response models," Econometrics and Statistics, Elsevier, vol. 13(C), pages 125-136.
    20. Kim, Daeju & Kawano, Shuichi & Ninomiya, Yoshiyuki, 2023. "Smoothly varying regularization," Computational Statistics & Data Analysis, Elsevier, vol. 179(C).

    More about this item

    Keywords

    Functional data analysis; Function-on-function linear regression; Adaptive smoothing; Functional regression;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

    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:spr:compst:v:38:y:2023:i:1:d:10.1007_s00180-022-01223-6. 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.