Probability Theory and Related Fields

, Volume 116, Issue 1, pp 21–39 | Cite as

On minimax identification of nonparametric autoregressive models

  • Bernard Delyon
  • Anatoli Juditsky


We consider the problem of nonparametric identification for a multi-dimensional functional autoregression y t = f(y t −1, …,y t−d ) + e t on the basis of N observations of y t . In the case when the unknown nonlinear function f belongs to the Barron class, we propose an estimation algorithm which provides approximations of f with expected L2 accuracy O(N1/4ln1/4N). We also show that this approximation rate cannot be significantly improved.

The proposed algorithms are “computationally efficient”– the total number of elementary computations necessary to complete the estimate grows polynomially with N.

Mathematics Subject Classification (1991): 62M05, 62G07, 62M20 


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Copyright information

© Springer-Verlag Berlin Heidelberg 2000

Authors and Affiliations

  • Bernard Delyon
    • 1
  • Anatoli Juditsky
    • 2
  1. 1.IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France e-mail: delyon@math.univ-rennes1.frFR
  2. 2.INRIA Rhône-Alpes, 655 avenue de l'Europe 38330 Montbonnot Saint Martin, France e-mail: Anatoli.Iouditski@inrialpes.frFR

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