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Minimax and minimax adaptive estimation in multiplicative regression: locally bayesian approach
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  • Published: 13 March 2011

Minimax and minimax adaptive estimation in multiplicative regression: locally bayesian approach

  • M. Chichignoud1 

Probability Theory and Related Fields volume 153, pages 543–586 (2012)Cite this article

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Abstract

This paper deals with the non-parametric estimation in the regression with the multiplicative noise. Using the local polynomial fitting and the bayesian approach, we construct the minimax on isotropic Hölder class estimator. Next, applying Lepski’s method we propose an estimator which is optimally adaptive over the collection of isotropic Hölder classes. To prove the optimality of the proposed procedure, we establish in particular the exponential inequality for the deviation of locally bayesian estimator since the parameter estimated. These theoretical results are illustrated by simulation study.

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Authors and Affiliations

  1. Université Aix-Marseille 1, LATP, 39 rue Joliot Curie, 13453, Marseille cedex 13, France

    M. Chichignoud

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  1. M. Chichignoud
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Correspondence to M. Chichignoud.

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Chichignoud, M. Minimax and minimax adaptive estimation in multiplicative regression: locally bayesian approach. Probab. Theory Relat. Fields 153, 543–586 (2012). https://doi.org/10.1007/s00440-011-0354-7

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  • Received: 23 May 2010

  • Revised: 16 February 2011

  • Published: 13 March 2011

  • Issue Date: August 2012

  • DOI: https://doi.org/10.1007/s00440-011-0354-7

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Keywords

  • Local bayesian fitting
  • Multiplicative regression
  • Adaptive bandwidth selector
  • Lepski’s method
  • Optimality criterion

Mathematics Subject Classification (2000)

  • 62G08
  • 62G20
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