IDEAS home Printed from
   My bibliography  Save this article

Most-predictive design points for functional data predictors


  • F. Ferraty
  • P. Hall
  • P. Vieu


We suggest a way of reducing the very high dimension of a functional predictor, X, to a low number of dimensions chosen so as to give the best predictive performance. Specifically, if X is observed on a fine grid of design points t 1 ,…, t r , we propose a method for choosing a small subset of these, say t i 1 ,…, t i k , to optimize the prediction of a response variable, Y. The values t i j are referred to as the most predictive design points, or covariates, for a given value of k, and are computed using information contained in a set of independent observations (X i , Y i ) of (X, Y). The algorithm is based on local linear regression, and calculations can be accelerated using linear regression to preselect the design points. Boosting can be employed to further improve the predictive performance. We illustrate the usefulness of our ideas through simulations and examples drawn from chemometrics, and we develop theoretical arguments showing that the methodology can be applied successfully in a range of settings. Copyright 2010, Oxford University Press.

Suggested Citation

  • F. Ferraty & P. Hall & P. Vieu, 2010. "Most-predictive design points for functional data predictors," Biometrika, Biometrika Trust, vol. 97(4), pages 807-824.
  • Handle: RePEc:oup:biomet:v:97:y:2010:i:4:p:807-824

    Download full text from publisher

    File URL:
    Download Restriction: Access to full text is restricted to subscribers.

    As the access to this document is restricted, you may want to search for a different version of it.


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

    Cited by:

    1. repec:bla:istatr:v:85:y:2017:i:2:p:228-249 is not listed on IDEAS
    2. Zhang, Tao & Zhang, Qingzhao & Wang, Qihua, 2014. "Model detection for functional polynomial regression," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 183-197.
    3. Guochang Wang & Jianjun Zhou & Wuqing Wu & Min Chen, 2017. "Robust functional sliced inverse regression," Statistical Papers, Springer, vol. 58(1), pages 227-245, March.
    4. Germán Aneiros & Philippe Vieu, 2015. "Partial linear modelling with multi-functional covariates," Computational Statistics, Springer, vol. 30(3), pages 647-671, September.
    5. Diego Vidaurre & Concha Bielza & Pedro Larrañaga, 2012. "Lazy lasso for local regression," Computational Statistics, Springer, vol. 27(3), pages 531-550, September.
    6. repec:bla:jorssb:v:79:y:2017:i:3:p:859-876 is not listed on IDEAS
    7. Fraiman, Ricardo & Gimenez, Yanina & Svarc, Marcela, 2016. "Feature selection for functional data," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 191-208.
    8. Geenens, Gery, 2015. "Moments, errors, asymptotic normality and large deviation principle in nonparametric functional regression," Statistics & Probability Letters, Elsevier, vol. 107(C), pages 369-377.
    9. Matsui, Hidetoshi, 2014. "Variable and boundary selection for functional data via multiclass logistic regression modeling," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 176-185.
    10. Aldo Goia & Philippe Vieu, 2015. "A partitioned Single Functional Index Model," Computational Statistics, Springer, vol. 30(3), pages 673-692, September.
    11. repec:eee:csdana:v:122:y:2018:i:c:p:101-114 is not listed on IDEAS
    12. Matsui, Hidetoshi & Konishi, Sadanori, 2011. "Variable selection for functional regression models via the L1 regularization," Computational Statistics & Data Analysis, Elsevier, vol. 55(12), pages 3304-3310, December.
    13. repec:spr:compst:v:32:y:2017:i:3:d:10.1007_s00180-017-0746-y is not listed on IDEAS
    14. repec:spr:stpapr:v:58:y:2017:i:4:d:10.1007_s00362-015-0738-3 is not listed on IDEAS

    More about this item


    Access and download statistics


    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:oup:biomet:v:97:y:2010:i:4:p:807-824. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Oxford University Press) or (Christopher F. Baum). General contact details of provider: .

    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.

    We have no references for this item. You can help adding them by using 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.