IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v70y2014icp362-372.html
   My bibliography  Save this article

Estimator selection and combination in scalar-on-function regression

Author

Listed:
  • Goldsmith, Jeff
  • Scheipl, Fabian

Abstract

Scalar-on-function regression problems with continuous outcomes arise naturally in many settings, and a wealth of estimation methods now exist. Despite the clear differences in regression model assumptions, tuning parameter selection, and the incorporation of functional structure, it remains common to apply a single method to any dataset of interest. In this paper we develop tools for estimator selection and combination in the context of continuous scalar-on-function regression based on minimizing the cross-validated prediction error of the final estimator. A broad collection of functional and high-dimensional regression methods is used as a library of candidate estimators. We find that the performance of any single method relative to others can vary dramatically across datasets, but that the proposed cross-validation procedure is consistently among the top performers. Four real-data analyses using publicly available benchmark datasets are presented; code implementing these analyses and facilitating the application of proposed methods on future datasets is available in a web supplement.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:70:y:2014:i:c:p:362-372
    DOI: 10.1016/j.csda.2013.10.009
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947313003629
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2013.10.009?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. 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.
    2. Lindquist, Martin A. & McKeague, Ian W., 2009. "Logistic Regression With Brownian-Like Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 104(488), pages 1575-1585.
    3. Reiss Philip T. & Huang Lei & Mennes Maarten, 2010. "Fast Function-on-Scalar Regression with Penalized Basis Expansions," The International Journal of Biostatistics, De Gruyter, vol. 6(1), pages 1-30, August.
    4. Febrero-Bande, Manuel & de la Fuente, Manuel Oviedo, 2012. "Statistical Computing in Functional Data Analysis: The R Package fda.usc," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 51(i04).
    5. Amato, U. & Antoniadis, A. & De Feis, I., 2006. "Dimension reduction in functional regression with applications," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2422-2446, May.
    6. van der Laan Mark J. & Polley Eric C & Hubbard Alan E., 2007. "Super Learner," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 6(1), pages 1-23, September.
    7. 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.
    8. 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).
    9. Friedman, Jerome H. & Hastie, Trevor & Tibshirani, Rob, 2010. "Regularization Paths for Generalized Linear Models via Coordinate Descent," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 33(i01).
    10. Ferraty, Frédéric & Vieu, Philippe, 2009. "Additive prediction and boosting for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1400-1413, February.
    11. Fang Yao & Hans-Georg Müller, 2010. "Functional quadratic regression," Biometrika, Biometrika Trust, vol. 97(1), pages 49-64.
    12. 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.
    13. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    14. Scheipl, Fabian, 2011. "spikeSlabGAM: Bayesian Variable Selection, Model Choice and Regularization for Generalized Additive Mixed Models in R," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 43(i14).
    15. 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.
    16. James, Gareth M. & Silverman, Bernard W., 2005. "Functional Adaptive Model Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 565-576, June.
    17. Laan Mark J. van der & Dudoit Sandrine & Vaart Aad W. van der, 2006. "The cross-validated adaptive epsilon-net estimator," Statistics & Risk Modeling, De Gruyter, vol. 24(3), pages 373-395, December.
    18. Aneiros-Pérez, Germán & Vieu, Philippe, 2006. "Semi-functional partial linear regression," Statistics & Probability Letters, Elsevier, vol. 76(11), pages 1102-1110, June.
    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. Zhang, Yaotian & Feng, Mingming & Shang, Ke-ke & Ran, Yijun & Wang, Cheng-Jun, 2022. "Peeking strategy for online news diffusion prediction via machine learning," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 598(C).
    3. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    4. Kalogridis, Ioannis & Van Aelst, Stefan, 2019. "Robust functional regression based on principal components," Journal of Multivariate Analysis, Elsevier, vol. 173(C), pages 393-415.
    5. Ahn, Kyungmin & Tucker, J. Derek & Wu, Wei & Srivastava, Anuj, 2020. "Regression models using shapes of functions as predictors," Computational Statistics & Data Analysis, Elsevier, vol. 151(C).
    6. Fraiman, Ricardo & Gimenez, Yanina & Svarc, Marcela, 2016. "Feature selection for functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 191-208.
    7. 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.

    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. Usset, Joseph & Staicu, Ana-Maria & Maity, Arnab, 2016. "Interaction models for functional regression," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 317-329.
    3. 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.
    4. M. D. Ruiz-Medina & D. Miranda & R. M. Espejo, 2019. "Dynamical multiple regression in function spaces, under kernel regressors, with ARH(1) errors," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 943-968, 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.
    6. Zhu, Hanbing & Zhang, Riquan & Yu, Zhou & Lian, Heng & Liu, Yanghui, 2019. "Estimation and testing for partially functional linear errors-in-variables models," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 296-314.
    7. Álvarez-Liébana, J. & Bosq, D. & Ruiz-Medina, M.D., 2017. "Asymptotic properties of a component-wise ARH(1) plug-in predictor," Journal of Multivariate Analysis, Elsevier, vol. 155(C), pages 12-34.
    8. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    9. Ciarleglio, Adam & Todd Ogden, R., 2016. "Wavelet-based scalar-on-function finite mixture regression models," Computational Statistics & Data Analysis, Elsevier, vol. 93(C), pages 86-96.
    10. 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.
    11. Eduardo García‐Portugués & Javier Álvarez‐Liébana & Gonzalo Álvarez‐Pérez & Wenceslao González‐Manteiga, 2021. "A goodness‐of‐fit test for the functional linear model with functional response," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 48(2), pages 502-528, June.
    12. Han Shang, 2014. "Bayesian bandwidth estimation for a semi-functional partial linear regression model with unknown error density," Computational Statistics, Springer, vol. 29(3), pages 829-848, June.
    13. 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.
    14. Ruiz-Medina, María D. & Álvarez-Liébana, Javier, 2019. "Strongly consistent autoregressive predictors in abstract Banach spaces," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 186-201.
    15. Han Lin Shang, 2014. "Bayesian bandwidth estimation for a functional nonparametric regression model with mixed types of regressors and unknown error density," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(3), pages 599-615, September.
    16. Boumahdi, Mounir & Ouassou, Idir & Rachdi, Mustapha, 2023. "Estimation in nonparametric functional-on-functional models with surrogate responses," Journal of Multivariate Analysis, Elsevier, vol. 198(C).
    17. Wang, Guochang & Lin, Nan & Zhang, Baoxue, 2014. "Functional k-means inverse regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 172-182.
    18. Ahmedou, Aziza & Marion, Jean-Marie & Pumo, Besnik, 2016. "Generalized linear model with functional predictors and their derivatives," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 313-324.
    19. Wang, Shaoli & Huang, Mian & Wu, Xing & Yao, Weixin, 2016. "Mixture of functional linear models and its application to CO2-GDP functional data," Computational Statistics & Data Analysis, Elsevier, vol. 97(C), pages 1-15.
    20. Silvia Novo & Germán Aneiros & Philippe Vieu, 2021. "Sparse semiparametric regression when predictors are mixture of functional and high-dimensional variables," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 481-504, 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:eee:csdana:v:70:y:2014:i:c:p:362-372. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.