A universal procedure for aggregating estimators

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In this paper we study the aggregation problem that can be formulated as follows. Assume that we have a family of estimators F built on the basis of available observations. The goal is to construct a new estimator whose risk is as close as possible to that of the best estimator in the family. We propose a general aggregation scheme that is universal in the following sense: it applies for families of arbitrary estimators and a wide variety of models and global risk measures. The procedure is based on comparison of empirical estimates of certain linear functionals with estimates induced by the family F . We derive oracle inequalities and show that they are unimprovable in some sense. Numerical results demonstrate good practical behavior of the procedure.

Original languageEnglish
Pages (from-to)542-568
Number of pages27
JournalAnnals of Statistics
Issue number1
StatePublished - Feb 2009


  • Aggregation
  • Lower bound
  • Normal means model
  • Oracle inequalities
  • Sparse vectors
  • White noise model

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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