Work

SPADES and mixture models

Year: 2010

Type: article

Abstract: 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 [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.

Source: The Annals of Statistics

DOI: 10.1214/09-aos790

Authors: Florentina Bunea, Alexandre B. Tsybakov, Marten H. Wegkamp, Adrian Barbu

Institutions: Florida State University, Université Pierre-et-Marie-Curie, University of Cambridge

Language: English

Topic: Statistical Methods and Inference

Subfield: Statistics and Probability

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funders: National Science Foundation, Isaac Newton Institute for Mathematical Sciences, Agence Nationale de la Recherche, Division of Mathematical Sciences

Awards: Adaptation, tests multiples, ranking et applications, Sparsity oracle inequalities via l_1 regularization in nonparametric models