Structural adaptation via double-struck Lp-norm oracle inequalities

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In this paper we study the problem of adaptive estimation of a multivariate function satisfying some structural assumption. We propose a novel estimation procedure that adapts simultaneously to unknown structure and smoothness of the underlying function. The problem of structural adaptation is stated as the problem of selection from a given collection of estimators. We develop a general selection rule and establish for it global oracle inequalities under arbitrary double-struck Lp-losses. These results are applied for adaptive estimation in the additive multi-index model.

Original languageEnglish
Pages (from-to)41-71
Number of pages31
JournalProbability Theory and Related Fields
Issue number1-2
StatePublished - Jan 2009

Bibliographical note

Funding Information:
Supported by the ISF grant No. 389/07.


  • Adaptive estimation
  • Minimax risk
  • Optimal rates of convergence
  • Oracle inequalities
  • Structural adaptation

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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