Risk bounds in isotonic regression

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Nonasymptotic risk bounds are provided for maximum likelihood-type isotonic estimators of an unknown nondecreasing regression function, with general average loss at design points. These bounds are optimal up to scale constants, and they imply uniform n-1/3-consistency of the ℓ p risk for unknown regression functions of uniformly bounded variation, under mild assumptions on the joint probability distribution of the data, with possibly dependent observations.

Original languageEnglish (US)
Pages (from-to)528-555
Number of pages28
JournalAnnals of Statistics
Issue number2
StatePublished - Apr 1 2002

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


  • Isotonic regression
  • Least squares estimator
  • Maximum likelihood estimator
  • Nonparametric regression
  • Risk bounds

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