Open Access
2014 Estimation and variable selection with exponential weights
Ery Arias-Castro, Karim Lounici
Electron. J. Statist. 8(1): 328-354 (2014). DOI: 10.1214/14-EJS883

Abstract

In the context of a linear model with a sparse coefficient vector, exponential weights methods have been shown to be achieve oracle inequalities for denoising/prediction. We show that such methods also succeed at variable selection and estimation under the near minimum condition on the design matrix, instead of much stronger assumptions required by other methods such as the Lasso or the Dantzig Selector. The same analysis yields consistency results for Bayesian methods and BIC-type variable selection under similar conditions.

Citation

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Ery Arias-Castro. Karim Lounici. "Estimation and variable selection with exponential weights." Electron. J. Statist. 8 (1) 328 - 354, 2014. https://doi.org/10.1214/14-EJS883

Information

Published: 2014
First available in Project Euclid: 18 April 2014

zbMATH: 1294.62164
MathSciNet: MR3195119
Digital Object Identifier: 10.1214/14-EJS883

Subjects:
Primary: 62J99

Keywords: estimation , Exponential weights , Gibbs sampler , identifiability condition , Model selection , sparse linear model , Variable selection

Rights: Copyright © 2014 The Institute of Mathematical Statistics and the Bernoulli Society

Vol.8 • No. 1 • 2014
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