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Confidence and prediction intervals in semi-functional partial linear regression

  • Paula Raña
  • Germán Aneiros
  • Philippe Vieu
  • Juan Vilar
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

Semi-functional partial linear regression model allows to deal with a nonparametric and a linear component within the functional regression. Naïve and wild bootstrap procedures are proposed to approximate the distribution of the estimators for each component in the model, and their asymptotic validities are obtained in the context of dependence data, under α-mixing conditions. Based on that bootstrap procedures, confidence intervals can be obtained for each component in the model, which can be also extended to deal with prediction intervals and prediction densities.

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References

  1. 1.
    Aneiros-Pérez, G., Vieu, P.: Semi-functional partial linear regression. Statist. Probab. Lett. 76, 1102–1110 (2006)Google Scholar
  2. 2.
    Aneiros-Pérez, G., Vieu, P.: Nonparametric time series prediction: A semifunctional partial linear modeling. J. Multivariate Anal. 99, 834–857 (2008)Google Scholar
  3. 3.
    Aneiros, G., Vilar, J., Raña, P.: Short-term forecast of daily curves of electricity demand and price. Electr. Power. Energy. Syst. 80, 96–108 (2016)Google Scholar
  4. 4.
    Ferraty, F., Van Keilegom, I., Vieu, P.: On the validity of the bootstrap in non-parametric functional regression. Scand. J. Statist. 37, 286–306 (2010)Google Scholar
  5. 5.
    Ferraty, F., Vieu, P.: Nonparametric functional data analysis. Springer-Verlag, New York (2006)Google Scholar
  6. 6.
    González-Manteiga, W., Mart´ınez-Calvo, A.: Bootstrap in functional linear regression. J. Statist. Plann. Inference 141, 453–461 (2011)Google Scholar
  7. 7.
    Horváth, L., Kokoszka, P.: Inference for functional data with applications. Springer Series in Statistics. Springer, New York (2012)Google Scholar
  8. 8.
    Hsing, T., Eubank, R.: Theoretical foundations of functional data analysis, with an introduction to linear operators. Wiley Series in Probability and Statistics. John Wiley & Sons, Chichester (2015)Google Scholar
  9. 9.
    Liang, H., Härdle, W., Sommerfeld, V.: Bootstrap approximation in a partially linear regression model. J. Statist. Plann. Inference 91, 413–426 (2000)Google Scholar
  10. 10.
    Raña, P.: Pointwise forecast, confidence and prediction intervals in electricity demand and price. Doctoral Thesis. Universidade da Coruña (2016)Google Scholar
  11. 11.
    Raña, P., Aneiros, G., Vilar, J., Vieu, P.: Bootstrap confidence intervals in functional nonparametric regression under dependence. Electron. J. Statist. 10(2), 1973–1999 (2016)Google Scholar
  12. 12.
    You, J., Zhou, X.: Bootstrap approximation of a semiparametric partially linear model with autoregressive errors. Statist. Sinica 15, 117–133 (2005)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Paula Raña
    • 1
  • Germán Aneiros
    • 1
  • Philippe Vieu
    • 2
  • Juan Vilar
    • 1
  1. 1.Departamento de MatemáticasUniversidade da CoruñaA CoruñaSpain
  2. 2.Institut de MathématiquesUniversité Paul SabatierToulouseFrance

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