Adaptive de-noising of signals satisfying differential inequalities

Alexander Goldenshluger, Arkadi Nemirovski

Research output: Contribution to journalArticlepeer-review


The paper is devoted to spatial adaptive estimation of signals satisfying linear differential inequalities with an unknown differential operator of a given order. The classes of signals under consideration cover a wide variety of classes common to nonparametric regression. In particular, they contain the signals whose parameters of smoothness are not uniformly bounded, even locally. We develop an estimator which is optimal in order over a wide range of the classes and "discrete" global accuracy measures.

Original languageEnglish
Pages (from-to)872-889
Number of pages18
JournalIEEE Transactions on Information Theory
Issue number3
StatePublished - 1997
Externally publishedYes


  • Adaptation
  • Differential inequalities
  • Lower bounds
  • Minimax risk
  • Nonparametric estimation
  • Optimal in order estimators

ASJC Scopus subject areas

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences


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