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Model selection for regression on a fixed design
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  • Published: August 2000

Model selection for regression on a fixed design

  • Yannick Baraud1 

Probability Theory and Related Fields volume 117, pages 467–493 (2000)Cite this article

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Abstract.

We deal with the problem of estimating some unknown regression function involved in a regression framework with deterministic design points. For this end, we consider some collection of finite dimensional linear spaces (models) and the least-squares estimator built on a data driven selected model among this collection. This data driven choice is performed via the minimization of some penalized model selection criterion that generalizes on Mallows' C p . We provide non asymptotic risk bounds for the so-defined estimator from which we deduce adaptivity properties. Our results hold under mild moment conditions on the errors. The statement and the use of a new moment inequality for empirical processes is at the heart of the techniques involved in our approach.

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Authors and Affiliations

  1. DMA, Ecole Normale Supérieure, 45 rue d'Ulm, 75230 Paris Cedex 05, France. e-mail: yannick.baraud@ens.fr, , , , , , FR

    Yannick Baraud

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  1. Yannick Baraud
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Received: 2 July 1997 / Revised version: 20 September 1999 / Published online: 6 July 2000

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Baraud, Y. Model selection for regression on a fixed design. Probab Theory Relat Fields 117, 467–493 (2000). https://doi.org/10.1007/PL00008731

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  • Issue Date: August 2000

  • DOI: https://doi.org/10.1007/PL00008731

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  • Key words and phrases: Nonparametric regression – Least-squares estimator – Model selection – Adaptive estimation – Moment inequality – Concentration of measure – Empirical processes
  • Mathematics Subject Classification (1991): Primary 62G07; Secondary 62J02, 60E15
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