IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v30y2015i2p539-568.html
   My bibliography  Save this article

Penalized function-on-function regression

Author

Listed:
  • Andrada Ivanescu
  • Ana-Maria Staicu
  • Fabian Scheipl
  • Sonja Greven

Abstract

A general framework for smooth regression of a functional response on one or multiple functional predictors is proposed. Using the mixed model representation of penalized regression expands the scope of function-on-function regression to many realistic scenarios. In particular, the approach can accommodate a densely or sparsely sampled functional response as well as multiple functional predictors that are observed on the same or different domains than the functional response, on a dense or sparse grid, and with or without noise. It also allows for seamless integration of continuous or categorical covariates and provides approximate confidence intervals as a by-product of the mixed model inference. The proposed methods are accompanied by easy to use and robust software implemented in the pffr function of the R package refund. Methodological developments are general, but were inspired by and applied to a diffusion tensor imaging brain tractography dataset. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:2:p:539-568
    DOI: 10.1007/s00180-014-0548-4
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s00180-014-0548-4
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s00180-014-0548-4?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. Crainiceanu, Ciprian M. & Staicu, Ana-Maria & Di, Chong-Zhi, 2009. "Generalized Multilevel Functional Regression," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1550-1561.
    2. Ana-Maria Staicu & Ciprian M. Crainiceanu & Daniel S. Reich & David Ruppert, 2012. "Modeling Functional Data with Spatially Heterogeneous Shape Characteristics," Biometrics, The International Biometric Society, vol. 68(2), pages 331-343, June.
    3. Mariano J. Valderrama & Francisco A. Ocaña & Ana M. Aguilera & Francisco M. Ocaña-Peinado, 2010. "Forecasting Pollen Concentration by a Two-Step Functional Model," Biometrics, The International Biometric Society, vol. 66(2), pages 578-585, June.
    4. Florentina Bunea & Andrada E. Ivanescu & Marten H. Wegkamp, 2011. "Adaptive inference for the mean of a Gaussian process in functional data," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(4), pages 531-538, September.
    5. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521780506.
    6. Philip T. Reiss & R. Todd Ogden, 2009. "Smoothing parameter selection for a class of semiparametric linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 505-523, April.
    7. Ana Aguilera & Francisco Ocaña & Mariano Valderrama, 1999. "Forecasting with unequally spaced data by a functional principal component approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 233-253, June.
    8. Simon N. Wood, 2011. "Fast stable restricted maximum likelihood and marginal likelihood estimation of semiparametric generalized linear models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 3-36, January.
    9. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    10. Martin A. Lindquist, 2012. "Functional Causal Mediation Analysis With an Application to Brain Connectivity," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(500), pages 1297-1309, December.
    11. Ciprian M. Crainiceanu & David Ruppert, 2004. "Likelihood ratio tests in linear mixed models with one variance component," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 165-185, February.
    12. Krivobokova, Tatyana & Kauermann, Goran, 2007. "A Note on Penalized Spline Smoothing With Correlated Errors," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1328-1337, December.
    13. Ruppert,David & Wand,M. P. & Carroll,R. J., 2003. "Semiparametric Regression," Cambridge Books, Cambridge University Press, number 9780521785167.
    14. Ferraty, F. & Van Keilegom, I. & Vieu, P., 2012. "Regression when both response and predictor are functions," Journal of Multivariate Analysis, Elsevier, vol. 109(C), pages 10-28.
    15. Ferraty, F. & Van Keilegom, Ingrid & Vieu, P., 2012. "Regression when both response and predictor are functions," LIDAM Reprints ISBA 2012004, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    16. Gerda Claeskens & Tatyana Krivobokova & Jean D. Opsomer, 2009. "Asymptotic properties of penalized spline estimators," Biometrika, Biometrika Trust, vol. 96(3), pages 529-544.
    17. Aneiros-Pérez, Germán & Vieu, Philippe, 2008. "Nonparametric time series prediction: A semi-functional partial linear modeling," Journal of Multivariate Analysis, Elsevier, vol. 99(5), pages 834-857, May.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. 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.
    3. Li, Meng & Wang, Kehui & Maity, Arnab & Staicu, Ana-Maria, 2022. "Inference in functional linear quantile regression," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    4. Hernandez Roig, Harold Antonio & Aguilera Morillo, María del Carmen & Aguilera, Ana M. & Preda, Cristian, 2023. "Penalized function-on-function partial leastsquares regression," DES - Working Papers. Statistics and Econometrics. WS 37758, Universidad Carlos III de Madrid. Departamento de Estadística.
    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. 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.
    7. Zhou, Zhiyang, 2021. "Fast implementation of partial least squares for function-on-function regression," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    8. 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.
    9. 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.
    10. Anton Rask Lundborg & Rajen D. Shah & Jonas Peters, 2022. "Conditional independence testing in Hilbert spaces with applications to functional data analysis," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 1821-1850, November.
    11. Maistre, Samuel & Patilea, Valentin, 2020. "Testing for the significance of functional covariates," Journal of Multivariate Analysis, Elsevier, vol. 179(C).
    12. Ufuk Beyaztas & Han Lin Shang & Aylin Alin, 2022. "Function-on-Function Partial Quantile Regression," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(1), pages 149-174, March.
    13. Gina-Maria Pomann & Ana-Maria Staicu & Sujit Ghosh, 2016. "A two-sample distribution-free test for functional data with application to a diffusion tensor imaging study of multiple sclerosis," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 65(3), pages 395-414, April.
    14. 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.

    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. 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.
    2. Philip T. Reiss & Lei Huang & Pei‐Shien Wu & Huaihou Chen & Stan Colcombe, 2017. "Pointwise influence matrices for functional‐response regression," Biometrics, The International Biometric Society, vol. 73(4), pages 1092-1101, December.
    3. Christian Schellhase & Göran Kauermann, 2012. "Density estimation and comparison with a penalized mixture approach," Computational Statistics, Springer, vol. 27(4), pages 757-777, December.
    4. Reiss Philip T. & Huang Lei, 2012. "Smoothness Selection for Penalized Quantile Regression Splines," The International Journal of Biostatistics, De Gruyter, vol. 8(1), pages 1-27, May.
    5. Roel Verbelen & Katrien Antonio & Gerda Claeskens, 2018. "Unravelling the predictive power of telematics data in car insurance pricing," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 67(5), pages 1275-1304, November.
    6. Goldsmith, Jeff & Scheipl, Fabian, 2014. "Estimator selection and combination in scalar-on-function regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 362-372.
    7. Huaihou Chen & Philip T. Reiss & Thaddeus Tarpey, 2014. "Optimally weighted L-super-2 distance for functional data," Biometrics, The International Biometric Society, vol. 70(3), pages 516-525, September.
    8. Zanin, Luca & Marra, Giampiero, 2012. "Assessing the functional relationship between CO2 emissions and economic development using an additive mixed model approach," Economic Modelling, Elsevier, vol. 29(4), pages 1328-1337.
    9. Sonja Greven & Ciprian Crainiceanu, 2013. "On likelihood ratio testing for penalized splines," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(4), pages 387-402, October.
    10. Blöchl, Andreas, 2014. "Trend Estimation with Penalized Splines as Mixed Models for Series with Structural Breaks," Discussion Papers in Economics 18446, University of Munich, Department of Economics.
    11. Lauren N. Berry & Nathaniel E. Helwig, 2021. "Cross-Validation, Information Theory, or Maximum Likelihood? A Comparison of Tuning Methods for Penalized Splines," Stats, MDPI, vol. 4(3), pages 1-24, September.
    12. Chen, Haiqiang & Fang, Ying & Li, Yingxing, 2015. "Estimation And Inference For Varying-Coefficient Models With Nonstationary Regressors Using Penalized Splines," Econometric Theory, Cambridge University Press, vol. 31(4), pages 753-777, August.
    13. Feng, Yuanhua & Härdle, Wolfgang Karl, 2020. "A data-driven P-spline smoother and the P-Spline-GARCH models," IRTG 1792 Discussion Papers 2020-016, Humboldt University of Berlin, International Research Training Group 1792 "High Dimensional Nonstationary Time Series".
    14. repec:wyi:journl:002195 is not listed on IDEAS
    15. Huaihou Chen & Yuanjia Wang, 2011. "A Penalized Spline Approach to Functional Mixed Effects Model Analysis," Biometrics, The International Biometric Society, vol. 67(3), pages 861-870, September.
    16. Philip T. Reiss & R. Todd Ogden, 2010. "Functional Generalized Linear Models with Images as Predictors," Biometrics, The International Biometric Society, vol. 66(1), pages 61-69, March.
    17. Øystein Sørensen & Anders M. Fjell & Kristine B. Walhovd, 2023. "Longitudinal Modeling of Age-Dependent Latent Traits with Generalized Additive Latent and Mixed Models," Psychometrika, Springer;The Psychometric Society, vol. 88(2), pages 456-486, June.
    18. Peter Pütz & Thomas Kneib, 2018. "A penalized spline estimator for fixed effects panel data models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 102(2), pages 145-166, April.
    19. Simon N. Wood & Zheyuan Li & Gavin Shaddick & Nicole H. Augustin, 2017. "Generalized Additive Models for Gigadata: Modeling the U.K. Black Smoke Network Daily Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(519), pages 1199-1210, July.
    20. Bloechl, Andreas, 2014. "Penalized Splines, Mixed Models and the Wiener-Kolmogorov Filter," Discussion Papers in Economics 21406, University of Munich, Department of Economics.
    21. Simon N. Wood, 2020. "Inference and computation with generalized additive models and their extensions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 29(2), pages 307-339, June.

    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:30:y:2015:i:2:p:539-568. 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.