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Article Dans Une Revue Annals of Statistics Année : 2010

SPADES and mixture models

F. Bunea
  • Fonction : Auteur
M.H. Wegkamp
  • Fonction : Auteur
A. Barbu
  • Fonction : Auteur

Résumé

This paper studies sparse density estimation via l(1) penalization (SPADES). We focus on estimation in high-dimensional mixture models and nonparametric adaptive density estimation. We show, respectively, that SPADES can recover, with high probability, the unknown components of a mixture of probability densities and that it yields minimax adaptive density estimates. These results are based on a general sparsity oracle inequality that the SPADES estimates satisfy. We offer a data driven method for the choice of the tuning parameter used in the construction of SPADES. The method uses the generalized bisection method first introduced in [10]. The suggested procedure bypasses the need for a grid search and offers substantial computational savings. We complement our theoretical results with a simulation study that employs this method for approximations of one and two-dimensional densities with mixtures. The numerical results strongly support our theoretical findings.

Dates et versions

hal-00514124 , version 1 (01-09-2010)

Identifiants

Citer

A.B. Tsybakov, F. Bunea, M.H. Wegkamp, A. Barbu. SPADES and mixture models. Annals of Statistics, 2010, 38 (4), pp.2525-2558. ⟨10.1214/09-AOS790⟩. ⟨hal-00514124⟩
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