Sparsity considerations for dependent observations

Details Sparsity considerations for dependent observations Sparsity considerations for dependent observations

2011-02-08

arxiv.org/abs/1102.1615v5

Electronic Journal of Statistics 5 (2011) pp 750-774

Mathematics

Statistics Theory

Scientific paper

10.1214/11-EJS626

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.

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