Advertisement

Robust Nonparametric Estimation for Functional Spatial Regression

  • Mohammed K. Attouch
  • Abdelkader Gheriballah
  • Ali Laksaci
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

This contribution deals with robust nonparametric regression analysis when the regressors are functional random fields. More precisely, we propose a family of robust nonparametric estimators for nonparametric functional spatial regression based on the kernel method. The main results of this work are the establishment of the almost complete convergence rate of these estimators.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Attouch, M., Laksaci, A., Ould Sa¨ıd, E.: Asymptotic normality of a robust estimator of the regression function for functional time series data. J. Korean Stat. Soc. 39, 489–500 (2010)Google Scholar
  2. 2.
    Azzedine, N., Laksaci, A., Ould Sa¨ıd, E.: On the robust nonparametric regression estimation for functional regressor. Stat. Probab. Lett. 78, 3216–3221 (2008)Google Scholar
  3. 3.
    Biau, G., Cadre, B.: Nonparametric Spatial Prediction. Stat. Infer. Stoch. Proc. 7, 327–349 (2004)MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Boente, G., Fraiman, R.: Nonparametric regression estimation. J. Multivariate Anal. 29, 180– 198 (1989)MathSciNetMATHGoogle Scholar
  5. 5.
    Boente, G., Gonzalez-Manteiga, W., Gonzalez, A.: Robust nonparametric estimation with missing data. J. Stat. Plan. Infer. 139, 571–592 (2009)MATHCrossRefGoogle Scholar
  6. 6.
    Bosq, D.: Linear processes in function spaces. Theory and Application. Lectures Notes in Statistics, 149, Springer Verlag, New-York (2000)Google Scholar
  7. 7.
    Carbon, M., Francq, C., Tran, L.T.: Kernel regression estimation for random fields. J. Stat. Plan. Infer. 137, 778–798 (2007)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Collomb, G., H¨ardle, W.: Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations. Stoch. Proc. Appl. 23, 77–89 (1986)Google Scholar
  9. 9.
    Crambes, C, Delsol, L., Laksaci, A.: Robust nonparametric estimation for functional data. J. Nonparametr. Stat. 20, 573–598 (2008)Google Scholar
  10. 10.
    Gheriballah, A., Laksaci, A., Rouane, R.: Robust nonparametric estimation for spatial regression. J. Stat. Plan. Infer. 140, 1656–1670 (2010)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Guyon, X.: Estimation d’un champ par pseudo-vraisemblance conditionnelle: Etude asymptotique et application au cas Markovien. Proceedings of the Sixth Franco-Belgian Meeting of Statisticia (1987)Google Scholar
  12. 12.
    Fan, J., Hu, T.C., Truong, Y.K.: Robust nonparametric function estimation. Scand. J. Stat. 21, 433–446 (1994)MathSciNetMATHGoogle Scholar
  13. 13.
    Ferraty, F., Vieu, P.: Nonparametric functional data analysis: Theory and Practice. Springer, New York (2006)MATHGoogle Scholar
  14. 14.
    Huber, P.J.: Robust estimation of a location parameter. Ann. Math. Stat. 35, 73–101 (1964)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    La¨ıb, N., Ould-Sa¨ıd, E.: A robust nonparametric estimation of the autoregression functionunder an ergodic hypothesis. Canad. J. Stat. 28, 817–828 (2000)Google Scholar
  16. 16.
    Li, J., Tran, L.T.: Nonparametric estimation of conditional expectation. J. Stat. Plan. Infer. 139, 164–175 (2009)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Ramsay, J. O., Silverman, B. W.: Functional data analysis (Second Edition). Springer, New York (2005)Google Scholar
  18. 18.
    Robinson, R.: Robust Nonparametric Autoregression. Lecture Notes in Statistics, 26, Springer Verlag, New York (1984)Google Scholar
  19. 19.
    Tran, L.T.: Kernel density estimation on random fields. J.Multivariate Anal. 34, 37–53 (1990)MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Mohammed K. Attouch
    • 1
  • Abdelkader Gheriballah
    • 1
  • Ali Laksaci
    • 1
  1. 1.Université de Sidi Bel AbbèsSidi Bel AbbèsAlgeria

Personalised recommendations