Electronic Journal of Statistics

Sparsity considerations for dependent variables

Pierre Alquier and Paul Doukhan

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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.

Article information

Electron. J. Statist., Volume 5 (2011), 750-774.

First available in Project Euclid: 8 August 2011

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62J07: Ridge regression; shrinkage estimators
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62J05: Linear regression 62G07: Density estimation 62G08: Nonparametric regression

Estimation in high dimension weak dependence sparsity deviation of empirical mean penalization LASSO regression estimation density estimation


Alquier, Pierre; Doukhan, Paul. Sparsity considerations for dependent variables. Electron. J. Statist. 5 (2011), 750--774. doi:10.1214/11-EJS626. https://projecteuclid.org/euclid.ejs/1312818917

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