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Presmoothing in Functional Linear Regression

  • Adela Martínez-Calvo
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We consider the functional linear model with scalar response Yand explanatory variable Xvalued in a functional space. Functional Principal Components Analysis (FPCA) have been used to estimate the model parameter in recent literature. We propose to modify this methodology by presmoothing either Xor Y. For these new estimates, consistency is stated and their efficiency by comparison with the FPCA approach are studied.

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References

  1. [1]
    Cai, T.T. and Hall, P.: Prediction in functional linear regression. Annals of Statistics 34,2159-2179(2006).zbMATHCrossRefMathSciNetGoogle Scholar
  2. [2]
    Cardot, H., Ferraty, F. and Sarda, P.: Functional linear model. Statistics and Prob-ability Letters 45 (1), 11-22 (1999).zbMATHCrossRefMathSciNetGoogle Scholar
  3. [3]
    Cardot, H., Ferraty, F. and Sarda, P.: Spline estimators for the functional linear model. Statistica Sinica 13 (3), 571-591 (2003).zbMATHMathSciNetGoogle Scholar
  4. [4]
    Crambes, C., Kneip, A. and Sarda, P.: Smoothing splines estimators for functional linear regression. submitted to Annals of Statistics.Google Scholar
  5. [5]
    Cristóbal-Cristóbal, J. A., Faraldo-Roca, P. and González-Manteiga, W.: A class of linear regression parameter estimators constructed by nonparametric estimation. Annals of Statistics 15 (2), 603-609 (1987).CrossRefMathSciNetGoogle Scholar
  6. [6]
    Faraldo-Roca, P. and González-Manteiga, W.: On e ciency of a new class of linear regression estimates obtained by preliminary non-parametric estimation. New Per-spectives in Theoretical and Applied Statistics (New York) (M. Puri, ed.), Wiley. 229 242 (1985).Google Scholar
  7. [7]
    Ferraty, F., Mas, A. and Vieu, P.: Nonparametric regression on functional data : inference and practical aspects. Australian and New Zealand Journal of Statistics 49(3),267-286 (2007).zbMATHCrossRefMathSciNetGoogle Scholar
  8. [8]
    Ferraty, F. and Vieu, P: Nonparametric functional data analysis : theory and practice. Springer, New York. (2006).zbMATHGoogle Scholar
  9. [9]
    Hall, P and Horowitz, J.L.: Methodology and convergence rates for functional linear regression. Annals of Statistics 35 (1), 70-91 (2007).zbMATHCrossRefMathSciNetGoogle Scholar
  10. [10]
    Hall, P. and Hosseini-Nasab, M.: On properties of functional principal components analysis. Journal of the Royal Statistical Society: Series B. 68 (1), 109-126 (2006).zbMATHCrossRefMathSciNetGoogle Scholar
  11. [11]
    Pezzulli, S. and Silverman, B.W.: Some properties of smoothed principal components analysis for functional data. Computational Statistics. 8, 1-16 (1993).zbMATHMathSciNetGoogle Scholar
  12. [12]
    Ramsay, J.O. and Silverman, B.W.: Functional data analysis. Springer, New York. (2005).Google Scholar
  13. [13]
    Silverman, B.W.: Smoothed functional principal components analysis by choice of norm. Annals of Statistics 24 (1), 1-24 (1996).zbMATHCrossRefMathSciNetGoogle Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Adela Martínez-Calvo
    • 1
  1. 1.University of Santiago de CompostelaSpain

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