Generalized Additive Models for Functional Data

  • Manuel Febrero-Bande
  • Wenceslao Gonzàlez-Manteiga
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)


The aim of this paper is to extend the ideas of generalized additive models for multivariate data (with known or unknown link function) to functional data covariates. The proposed algorithmis a modified version of the local scoring and backfitting algorithms that allows for the non-parametric estimation of the link function. This algorithm would be applied to predict a binary response example.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aneiros-P´erez, G., Vieu, P.: Semi-functional partial linear regression. Stat. Probabil. Lett. 76, 1102–1110 (2006)Google Scholar
  2. 2.
    Cardot, H., Sarda, P.: Estimation in generalized linear models for functional data via penalized likelihood. J. Multivariate Anal. 92 (1), 24–41 (2005)MathSciNetMATHCrossRefGoogle Scholar
  3. 3.
    Escabias, M., Aguilera, A.M., Valderrama, M.J.: Principal component estimation of functional logistic regression: discussion of two different approaches. J. Nonparametr. Stat. 16 (3–4), 365–384 (2004)MathSciNetMATHGoogle Scholar
  4. 4.
    Escabias, M., Aguilera, A.M., Valderrama, M.J.: Functional PLS logit regression model. Comput. Stat. Data An. 51, 4891–4902 (2006)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Ferray, F., Vieu, P.: Nonparametric functional data analysis. Springer, New York (2006) 6. Horowitz, J.L.: Semiparametric Methods in Econometrics. Lecture Notes in Statistics, 131, Springer Verlag (1998)Google Scholar
  6. 6.
    Horowitz, J.L.: Nonparametric estimation of a generalized additive model with an unknown link function. Econometrica 69, 499–514 (2001)MathSciNetMATHCrossRefGoogle Scholar
  7. 7.
    McCullagh, P., Nelder, J.A.: Generalized Linear Models. Chapman & Hall (1989) 9. M¨uller, H.G., Yao, F.: Functional Additive Model. J. Am. Stat. Assoc. 103 (484), 1534–1544 (2008)Google Scholar
  8. 8.
    Roca-Pardi˜nas, J., Gonz´alez-Manteiga, W., Febrero-Bande, M., Prada-S´anchez, J.M., Cadarso-Su´arez, C.: Predicting binary time series of SO2 using generalized additive models with unknown link function. Environmetrics 15, 729–742 (2004)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Manuel Febrero-Bande
    • 1
  • Wenceslao Gonzàlez-Manteiga
    • 1
  1. 1.University of Santiago de CompostelaSantiago de CompostelaSpain

Personalised recommendations