WIAS Preprint No. 1000, (2004)

Local likelihood modelling via stagewise aggregation



Authors

  • Belomestny, Denis
  • Spokoiny, Vladimir
    ORCID: 0000-0002-2040-3427

2010 Mathematics Subject Classification

  • 62G05 62G07 62G08 62H30

Keywords

  • aggregation, local likelihood, exponential family, density estimation, classification, spatial adaptivity

Abstract

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. Given a sequence of local likelihood estimates which we call "weak" estimates, the proposed method yields a new aggregated estimate whose pointwise risk does not exceed the smallest risk among all "weak" estimates multiplied by some logarithmic factor. We establish a number of important theoretical results concerning optimality of the aggregated estimate and show a good performance of the procedure in simulated examples.

Appeared in

  • Ann. Statist., 25 (2007) pp. 2287--2311.

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