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A Fast Functional Locally Modeled Conditional Density and Mode for Functional Time-Series

  • Jacques Demongeot
  • Ali Laksaci
  • Fethi Madani
  • Mustapha Rachdi
Conference paper
Part of the Contributions to Statistics book series (CONTRIB.STAT.)

Abstract

We study the asymptotic behavior of the nonparametric local linear estimation of the conditional density of a scalar response variable given a random variable taking values in a semi-metric space. Under some general conditions on the mixing property of the data, we establish the pointwise almost-complete convergence, with rates, of this estimator. Moreover, we give some particular cases of our results which can also be considered as novel in the finite dimensional setting: Nadaraya-Watson estimator, multivariate data and the independent and identically distributed data case. On the other hand, this approach is also applied in time-series analysis to the prediction problem via the conditional mode estimation.

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References

  1. Barrientos-Marin, J., Ferraty, F., Vieu, P.: Locally Modelled Regression and Functional Data.Google Scholar
  2. J. Nonparametr. Stat. 22, 617–632 (2010)Google Scholar
  3. Benhenni, K., Griche-Hedli, S., Rachdi, M.: Estimation of the regression operator from functionalGoogle Scholar
  4. fixed-design with correlated errors. J. Multivariate Anal. 101, 476–490 (2010)Google Scholar
  5. Benhenni, K., Ferraty, F., Rachdi, M., Vieu, P.: Local smoothing regression with functionalGoogle Scholar
  6. data. Computation. Stat. 22, 353–369 (2007)Google Scholar
  7. Ba`ıllo, A., Gran´e, A.: Local linear regression for functional predictor and scalar response. J.Google Scholar
  8. Multivariate Anal. 100, 102–111 (2009)Google Scholar
  9. Dabo-Niang, S., Laksaci, A.: Estimation non param´etrique du mode conditionnel pour variableGoogle Scholar
  10. explicative fonctionnelle. Pub. Inst. Stat. Univ. Paris 3, Pages 27–42 (2007)Google Scholar
  11. Demongeot, J., Laksaci, A., Madani, F., Rachdi,M.: Local linear estimation of the conditionalGoogle Scholar
  12. density for functional data. C. R., Math., Acad. Sci. Paris 348, 931–934 2010)Google Scholar
  13. Fan, J., Yim, T.-H.: A cross-validation method for estimating conditional densities.Google Scholar
  14. Biometrika 91, 819–834 (2004)Google Scholar
  15. Fan, J., Gijbels, I.: Local Polynomial Modelling and its Applications. Chapman & Hall, LondonGoogle Scholar
  16. Ferraty, F., Laksaci, A., Vieu, P.: Estimating some characteristics of the conditional distributionGoogle Scholar
  17. in nonparametric functional models. Stat. Infer. Stoch. Process. 9, 47–76 (2006)Google Scholar
  18. Ferraty, F., Vieu, P.: Nonparametric functional data analysis. Theory and Practice. Series inGoogle Scholar
  19. Statistics, Springer, New York (2006)Google Scholar
  20. Laksaci, A.: Convergence en moyenne quadratique de l’estimateur `a noyau de la densit´e conditionnelleGoogle Scholar
  21. avec variable explicative fonctionnelle. Pub. Inst. Stat. Univ. Paris 3, 69–80 (2007)Google Scholar
  22. Ouassou, I., Rachdi, M.: Stein type estimation of the regression operator for functional data.Google Scholar
  23. Advances and Applications in Statistical Sciences 1, 233–250 (2010)Google Scholar
  24. Rachdi, M., Vieu, P.: Nonparametric regression for functional data: automatic smoothing parameterGoogle Scholar
  25. selection. J. Statist. Plann. Inference 137, 2784–2801 (2007)Google Scholar
  26. Rio, E.: Th´eorie asymptotique des processus al´eatoires faiblement d´ependants. CollectionGoogle Scholar
  27. Math´ematiques et Applications, ESAIM, Springer (2000)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jacques Demongeot
    • 1
  • Ali Laksaci
    • 2
  • Fethi Madani
    • 3
  • Mustapha Rachdi
    • 3
  1. 1.Université J. FourierGrenobleFrance
  2. 2.Université Djillali LiabèsSidi Bel AbbèsAlgeria
  3. 3.Université P. Mendès FranceGrenobleFrance

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