General selection rule from a family of linear estimators

A. V. Goldenshluger, O. V. Lepski

Research output: Contribution to journalArticlepeer-review


In the framework of an abstract statistical model we propose a procedure for selecting an estimator from a given family of linear estimators. We derive an upper bound on the risk of the selected estimator and demonstrate how this result can be used in order to develop minimax and adaptive minimax estimators in specific nonparametric estimation problems.

Original languageEnglish
Pages (from-to)209-226
Number of pages18
JournalTheory of Probability and its Applications
Issue number2
StatePublished - 2013


  • Adaptive minimax estimation
  • Linear estimators
  • Majorant
  • Oracle inequality
  • Statistical experiment

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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