Open Access
2011 Sparsity considerations for dependent variables
Pierre Alquier, Paul Doukhan
Electron. J. Statist. 5: 750-774 (2011). DOI: 10.1214/11-EJS626


The aim of this paper is to provide a comprehensive introduction for the study of 1-penalized estimators in the context of dependent observations. We define a general 1-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO [Tib96] in the regression estimation setting. Powerful theoretical guarantees on the statistical performances of the LASSO were provided in recent papers, however, they usually only deal with the iid case. Here, we study this estimator under various dependence assumptions.


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Pierre Alquier. Paul Doukhan. "Sparsity considerations for dependent variables." Electron. J. Statist. 5 750 - 774, 2011.


Published: 2011
First available in Project Euclid: 8 August 2011

zbMATH: 1274.62462
MathSciNet: MR2824815
Digital Object Identifier: 10.1214/11-EJS626

Primary: 62J07
Secondary: 62G07 , 62G08 , 62J05 , 62M10

Keywords: Density estimation , deviation of empirical mean , Estimation in high dimension , Lasso , Penalization , Regression estimation , Sparsity , Weak dependence

Rights: Copyright © 2011 The Institute of Mathematical Statistics and the Bernoulli Society

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