Spatial aggregation of local likelihood estimates with applications to classification

Denis Belomestny, Vladimir Spokoiny

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

This paper presents a new method for spatially adaptive local (constant) likelihood estimation which applies to a broad class of nonparametric models, including the Gaussian, Poisson and binary response models. The main idea of the method is, given a sequence of local likelihood estimates ("weak" estimates), to construct a new aggregated estimate whose pointwise risk is of order of the smallest risk among all "weak" estimates.We also propose a new approach toward selecting the parameters of the procedure by providing the prescribed behavior of the resulting estimate in the simple parametric situation. We establish a number of important theoretical results concerning the optimality of the aggregated estimate. In particular, our "oracle" result claims that its risk is, up to some logarithmic multiplier, equal to the smallest risk for the given family of estimates. The performance of the procedure is illustrated by application to the classification problem. A numerical study demonstrates its reasonable performance in simulated and real-life examples.

Original languageEnglish
Pages (from-to)2287-2311
Number of pages25
JournalAnnals of Statistics
Volume35
Issue number5
DOIs
Publication statusPublished - Oct 2007
Externally publishedYes

Keywords

  • Adaptive weights
  • Classification
  • Exponential family
  • Local likelihood

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