On estimation of Lr -norms in Gaussian white noise models

Yanjun Han, Jiantao Jiao, Rajarshi Mukherjee

Research output: Contribution to journalArticlepeer-review


We provide a complete picture of asymptotically minimax estimation of Lr-norms (for any r≥ 1) of the mean in Gaussian white noise model over Nikolskii–Besov spaces. In this regard, we complement the work of Lepski et al. (Probab Theory Relat Fields 113(2):221–253, 1999), who considered the cases of r= 1 (with poly-logarithmic gap between upper and lower bounds) and r even (with asymptotically sharp upper and lower bounds) over Hölder spaces. We additionally consider the case of asymptotically adaptive minimax estimation and demonstrate a difference between even and non-even r in terms of an investigator’s ability to produce asymptotically adaptive minimax estimators without paying a penalty.

Original languageEnglish (US)
Pages (from-to)1243-1294
Number of pages52
JournalProbability Theory and Related Fields
Issue number3-4
StatePublished - Aug 1 2020


  • Besov spaces
  • Minimax rates
  • Non-smooth functional estimation
  • Polynomial approximation
  • Rational function approximation

ASJC Scopus subject areas

  • Analysis
  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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