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On minimax identification of nonparametric autoregressive models
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  • Published: January 2000

On minimax identification of nonparametric autoregressive models

  • Bernard Delyon1 &
  • Anatoli Juditsky2 

Probability Theory and Related Fields volume 116, pages 21–39 (2000)Cite this article

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  • 3 Citations

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Abstract.

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 L 2 accuracy O(N 1/4ln1/4 N). 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.

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Authors and Affiliations

  1. IRISA, Campus de Beaulieu, 35042 Rennes Cedex, France e-mail: delyon@math.univ-rennes1.fr, , , , , , FR

    Bernard Delyon

  2. INRIA Rhône-Alpes, 655 avenue de l'Europe 38330 Montbonnot Saint Martin, France e-mail: Anatoli.Iouditski@inrialpes.fr, , , , , , FR

    Anatoli Juditsky

Authors
  1. Bernard Delyon
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  2. Anatoli Juditsky
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Received: 23 September 1997 / Revised version: 28 January 1999

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Cite this article

Delyon, B., Juditsky, A. On minimax identification of nonparametric autoregressive models. Probab Theory Relat Fields 116, 21–39 (2000). https://doi.org/10.1007/PL00008721

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  • Issue Date: January 2000

  • DOI: https://doi.org/10.1007/PL00008721

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