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August 2010 SPADES and mixture models
Florentina Bunea, Alexandre B. Tsybakov, Marten H. Wegkamp, Adrian Barbu
Ann. Statist. 38(4): 2525-2558 (August 2010). DOI: 10.1214/09-AOS790


This paper studies sparse density estimation via 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.


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Florentina Bunea. Alexandre B. Tsybakov. Marten H. Wegkamp. Adrian Barbu. "SPADES and mixture models." Ann. Statist. 38 (4) 2525 - 2558, August 2010.


Published: August 2010
First available in Project Euclid: 11 July 2010

zbMATH: 1198.62025
MathSciNet: MR2676897
Digital Object Identifier: 10.1214/09-AOS790

Primary: 62G08
Secondary: 62C20 , 62G05 , 62G20

Keywords: adaptive estimation , Aggregation , consistent model selection , Lasso , minimax risk , Mixture models , Nonparametric density estimation , Oracle inequalities , penalized least squares , Sparsity , Statistical learning

Rights: Copyright © 2010 Institute of Mathematical Statistics


Vol.38 • No. 4 • August 2010
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