Some theoretical results on the Grouped Variables Lasso
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- 1 December 2008
- journal article
- Published by Allerton Press in Mathematical Methods of Statistics
- Vol. 17 (4) , 317-326
Abstract
We consider the linear regression model with Gaussian error. We estimate the unknown parameters by a procedure inspired by the Group Lasso estimator introduced in [22]. We show that this estimator satisfies a sparsity inequality, i.e., a bound in terms of the number of non-zero components of the oracle regression vector. We prove that this bound is better, in some cases, than the one achieved by the Lasso and the Dantzig selector.Keywords
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This publication has 20 references indexed in Scilit:
- The Group Lasso for Logistic RegressionJournal of the Royal Statistical Society Series B: Statistical Methodology, 2008
- Rejoinder: The Dantzig selector: Statistical estimation when p is much larger than nThe Annals of Statistics, 2007
- Relaxed LassoComputational Statistics & Data Analysis, 2007
- Aggregation for Gaussian regressionThe Annals of Statistics, 2007
- Sparse Density Estimation with ℓ1 Penalties2007
- Sparsity oracle inequalities for the LassoElectronic Journal of Statistics, 2007
- Stable recovery of sparse overcomplete representations in the presence of noiseIEEE Transactions on Information Theory, 2005
- Least angle regressionThe Annals of Statistics, 2004
- Variable Selection via Nonconcave Penalized Likelihood and its Oracle PropertiesJournal of the American Statistical Association, 2001
- Asymptotics for lasso-type estimatorsThe Annals of Statistics, 2000