Local Linear Functional Regression Based on Weighted Distance-based Regression

  • Eva Boj
  • Pedro Delicado
  • Josep Fortiana
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

We consider the problem of nonparametrically predicting a scalar response variable yfrom a functional predictor . We have nobservations ( i yi). We assign a weight wi= K(d(   i)h) to each i, where dis a semimetric, Kis a kernel function and his the bandwidth. Then we fit a Weighted (Linear) Distance-Based Regression, where the weights are as above and the distances are given by a possibly difierent semi-metric.


Weighted Little Square Weighted Version Mean Square Prediction Error Local Linear Regression Variable Bandwidth 
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]
    Baíllo, A. and Grané, A.: Local linear regression for functional predictor and scalar response, Univ. Carlos III de Madrid, Statistics and Econometric Series, 07-61 (2007).Google Scholar
  2. [2]
    Barrientos-Marin, Jorge .: Some Practical Problems of Recent Nonparametric Pro-cedures: Testing, Estimation, and Application. Univ. de Alicante (2007).Google Scholar
  3. [3]
    Berlinet,A.,Elamine, A. and Mas, A.: Local linear regres-sionforfunctionaldata",ArXive-prints.0710.5218,710, (2007).
  4. [4]
    E. Boj and Claramunt, M. M. and J. Fortiana.: Selection of Predictors in Distance-Based Regression. Comm. in Statistics. Simulation and Computation. 36, 87-98 (2007).MATHCrossRefGoogle Scholar
  5. [5]
    Boj, E. and Fortiana, J.: Weighted Distance-Based Regression, Unpublished (2007).Google Scholar
  6. [6]
    Borg, Ingwer and Groenen, Patrick .: Modern Multidimensional Scaling: Theory and Applications (2nd ed), Springer-Verlag, New York (2005).MATHGoogle Scholar
  7. [7]
    Cuadras, C. M. and Arenas, C.: A distance based regression model for prediction with mixed data. Comm. in Statistics A. Theory and Methods, 19, 2261-2279 (1990).CrossRefMathSciNetGoogle Scholar
  8. [8]
    Cuadras Carles M. and Josep Fortiana.: Distance-Based Multivariate Two Sample Tests IMUB. Institut de Matemàtica de la Universitat de Barcelona. 334 (2003).Google Scholar
  9. [9]
    Cuadras, C. M.: Distance Analysis in discrimination and classi cation using both continuous and categorical variables. dodge:1989, 459-473 (1989).Google Scholar
  10. [10]
    Cuadras, C. M., Arenas, C. and Fortiana, J.: Some computational aspects of a Distance-Based model for Prediction. Comm. in Statistics. Simulation and Com-putation 25, 593-609 (1996).MATHCrossRefGoogle Scholar
  11. [20]
    Ferraty F. and Vieu P.: Nonparametric modelling for functional data. Springer-Verlag, New York. (2006).Google Scholar
  12. [12]
    Ferraty, F., Mas, A. and Vieu, P.: Nonparametric regression on functional data: Inference and practical aspects. Australian and New Zeland J. Stats. 49 (3), 267-286 (2007).MATHCrossRefMathSciNetGoogle Scholar
  13. [13]
    Muñoz-Maldonado, Y., Staniswalis, J.G. and Irwin, L.N. and Byers, D.: A similarity analysis of curves. Canadian Journal of Statistics. 30, 373-381 (2002).MATHCrossRefGoogle Scholar
  14. [14]
    Ramsay, J. and Silverman, B.: Functional Data Analysis (Second Edition) Spinger-Verlag, New York. (2005).Google Scholar

Copyright information

© Physica-Verlag Heidelberg 2008

Authors and Affiliations

  • Eva Boj
    • 1
  • Pedro Delicado
    • 2
  • Josep Fortiana
    • 1
  1. 1.Universitat de BarcelonaSpain
  2. 2.Universitat Politècnica de CatalunyaSpain

Personalised recommendations