Propagation-separation approach for local likelihood estimation

Jörg Polzehl, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

118 Citations (Scopus)


The paper presents a unified approach to local likelihood estimation for a broad class of nonparametric models, including e.g. the regression, density, Poisson and binary response model. The method extends the adaptive weights smoothing (AWS) procedure introduced in Polzehl and Spokoiny (2000) in context of image denoising. The main idea of the method is to describe a greatest possible local neighborhood of every design point X i in which the local parametric assumption is justified by the data. The method is especially powerful for model functions having large homogeneous regions and sharp discontinuities. The performance of the proposed procedure is illustrated by numerical examples for density estimation and classification. We also establish some remarkable theoretical nonasymptotic results on properties of the new algorithm. This includes the ''propagation'' property which particularly yields the root-n consistency of the resulting estimate in the homogeneous case. We also state an ''oracle'' result which implies rate optimality of the estimate under usual smoothness conditions and a ''separation'' result which explains the sensitivity of the method to structural changes.

Original languageEnglish
Pages (from-to)335-362
Number of pages28
JournalProbability Theory and Related Fields
Issue number3
Publication statusPublished - Jul 2006
Externally publishedYes


  • Adaptive weights
  • Classification
  • Density estimation
  • Exponential family
  • Local likelihood
  • Propagation
  • Separation


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