Spatially adaptive density estimation by localised Haar projections

Florian Gach, Richard Nickl, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

8 Citations (Scopus)


Given a random sample from some unknown density f0 :ℝ →[0,∞) we devise Haar wavelet estimators for f0 with variable resolution levels constructed from localised test procedures (as in Lepski, Mammen and Spokoiny (Ann. Statist. 25 (1997) 927-947)). We show that these estimators satisfy an oracle inequality that adapts to heterogeneous smoothness of f0, simultaneously for every point x in a fixed interval, in sup-norm loss. The thresholding constants involved in the test procedures can be chosen in practice under the idealised assumption that the true density is locally constant in a neighborhood of the point x of estimation, and an information theoretic justification of this practise is given.

Original languageEnglish
Pages (from-to)900-914
Number of pages15
JournalAnnales de l'institut Henri Poincare (B) Probability and Statistics
Issue number3
Publication statusPublished - Aug 2013
Externally publishedYes


  • Propagation condition
  • Spatial adaptation


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