Influence in the Functional Linear Model with Scalar Response

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

This paper studies how to identify influential curves in the functional linear model in which the response is scalar and the predictor is functional and how to measure their effects on the estimation of the model and on the forecasts, when the model is estimated by the principal components method. For that, we introduce and analyze two statistics that measure the influence of each curve on the functional slope estimate of the model, which are generalizations of the measures proposed for the standard regression model by Cook (1977) and Peña (2005), respectively.


Scalar Response Functional Data Analysis Functional Principal Component Analysis Principal Component Method Functional Principal Component 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Cai, T. T. and Hall, P.: Prediction in functional linear regression. Annals of Statistics. 34,2159-2179 (2006).MATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Cardot, H., Ferraty, F. and Sarda, P.: Functional linear model. Statistics and Probability Letters. 45, 11-22 (1999).MATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Cardot, H., Ferraty, F. and Sarda, P.: Spline estimators for the functional linear model. Statistica Sinica. 13, 571-591 (2003).MATHMathSciNetGoogle Scholar
  4. [4]
    Chiou, J. M. and Müller, H. G.: Diagnostics for functional regression via residual processes. Computational Statistics and Data Analysis. 51, 4849-4863 (2007).MATHCrossRefMathSciNetGoogle Scholar
  5. [5]
    Cook, D. R.: Detection of in uential observations in linear regression. Technometrics. 19,15-18. (1977).MATHCrossRefMathSciNetGoogle Scholar
  6. [6]
    Ferraty, F. and Vieu, P.: Nonparametric functional data analysis. Springer-Verlag, New York (2006)MATHGoogle Scholar
  7. [7]
    Hall, P. and Hosseini-Nasab, M.: On properties of functional principal components analysis. Journal of the Royal Statistical Society, Series B. 68, 109-126 (2006).MATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Hall, P. and Horowitz, J. L.: Methodology and convergence rates for functional linear regression. Annals of Statistics. 35, 70-91 (2007).MATHCrossRefMathSciNetGoogle Scholar
  9. [9]
    Hastie, T. and Mallows, C.: A discussion of A statistical view of some chemometrics regression tools by I. E. Frank and J. H. Friedman. Technometrics. 35, 140-143 (1993).CrossRefGoogle Scholar
  10. [10]
    Marx, B. D. and Eilers, P. H.: Generalized linear regression on sampled signals and curves: a p-spline approach. Technometrics. 41, 1-13 (1999).CrossRefGoogle Scholar
  11. [11]
    Peña, D.: A new statistic for in uence in linear regression. Technometrics. 47, 1-12 (2005).CrossRefMathSciNetGoogle Scholar
  12. [12]
    Ramsay, J. O. and Silverman, B. W.: Applied Functional Data Analysis. Springer-Verlag, New York (2004).Google Scholar
  13. [13]
    Ramsay, J. O. and Silverman, B. W.: Functional data analysis, 2nd edition. Springer-Verlag, New York (2005).Google Scholar
  14. [14]
    Shen, Q. and Xu, H.: Diagnostics for linear models with functional responses. Technometrics. 49, 26-33 (2007).CrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Manuel Febrero
    • 1
  • Pedro Galeano
    • 1
  • Wenceslao González-Manteiga
    • 1
  1. 1.Departamento de Estadística e Investigación OperativaUniversidad de Santiago de CompostelaSpain

Personalised recommendations