The Annals of Statistics
- Ann. Statist.
- Volume 38, Number 4 (2010), 2525-2558.
SPADES and mixture models
This paper studies sparse density estimation via ℓ1 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 . 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.
Ann. Statist., Volume 38, Number 4 (2010), 2525-2558.
First available in Project Euclid: 11 July 2010
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Adaptive estimation aggregation lasso minimax risk mixture models consistent model selection nonparametric density estimation oracle inequalities penalized least squares sparsity statistical learning
Bunea, Florentina; Tsybakov, Alexandre B.; Wegkamp, Marten H.; Barbu, Adrian. SPADES and mixture models. Ann. Statist. 38 (2010), no. 4, 2525--2558. doi:10.1214/09-AOS790. https://projecteuclid.org/euclid.aos/1278861256