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

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


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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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Jacques Demongeot
    • 1
    Email author
  • 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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