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Mathematical Methods of Statistics

, Volume 23, Issue 1, pp 20–37 | Cite as

Concentration inequalities for the exponential weighting method

  • Yu. Golubev
  • D. Ostrovski
Article

Abstract

The paper is concerned with recovering an unknown vector from noisy data with the help of a family of ordered smoothers [11]. The estimators within this family are aggregated based on the exponential weighting method and the performance of the aggregated estimate is measured by the excess risk controlling deviation of the square losses from the oracle risk. Based on natural statistical properties of ordered smoothers, we propose a novel method for obtaining concentration inequalities for the exponential weighting method.

Keywords

ordered smoothers exponential weighting unbiased risk estimation oracle inequality concentration inequality 

2010 Mathematics Subject Classification

Primary 62C99 secondary 62C10, 62C20, 62J05. 

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Copyright information

© Allerton Press, Inc. 2014

Authors and Affiliations

  1. 1.Aix Marseille Univ.MarseilleFrance
  2. 2.Inst. for Inform. Transmission ProblemsMoscowRussia
  3. 3.Inst. of Physics and TechnologyMoscowRussia

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