Minimax rate adaptive estimation over continuous hyper-parameters

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We study minimax-rate adaptive estimation for density classes indexed by continuous hyper-parameters. The classes are assumed to be partially ordered in terms of inclusion relationship. Under a mild condition on the minimax risks, we show that a minimax-rate adaptive estimator can be constructed for the classes.

Original languageEnglish (US)
Pages (from-to)2081-2085
Number of pages5
JournalIEEE Transactions on Information Theory
Issue number5
StatePublished - Jul 2001


  • Adaptive density estimation
  • Combining procedures
  • Minimax-rate adaptation


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