hal-00564291, version 1
Sparsity considerations for dependent observations
(08/02/2011)
Abstract: The aim of this paper is to provide a comprehensive introduction for the study of L1-penalized estimators in the context of dependent observations. We define a general $\ell_{1}$-penalized estimator for solving problems of stochastic optimization. This estimator turns out to be the LASSO 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 our estimator under various dependence assumptions.
- 1:
- CNRS : UMR7599 – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Paris VII - Paris Diderot
- 2:
- INSEE – École Nationale de la Statistique et de l'Administration Économique
- 3:
- CNRS : UMR8088 – Université de Cergy Pontoise
- Domain : Mathematics/Statistics
Statistics/Statistics Theory - Keywords : Estimation in high dimensional – weak dependence – sparsity – penalization – LASSO – regression estimation – density estimation.
- Available versions : v1 (2011-02-08) v2 (2011-02-17) v3 (2011-02-24) v4 (2011-07-06) v5 (2011-08-07)
- hal-00564291, version 1
- http://hal.archives-ouvertes.fr/hal-00564291
- oai:hal.archives-ouvertes.fr:hal-00564291
- From:
- Submitted on: Tuesday, 8 February 2011 15:36:16
- Updated on: Tuesday, 8 February 2011 15:47:12
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