SOCP based variance free Dantzig selector with application to robust estimation

DOI10.1016/j.crma.2012.09.016zbMath1369.62162OpenAlexW2015154136MaRDI QIDQ715639

Arnak S. Dalalyan

Publication date: 31 October 2012

Published in: Comptes Rendus. Mathématique. Académie des Sciences, Paris (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.crma.2012.09.016

zbMATH Keywords

high dimensional linear regressionjoint estimation of sparse vector and noise variancenonasymptotic sharp risk boundssecond-order cone program (SOCP)

Mathematics Subject Classification ID

Ridge regression; shrinkage estimators (Lasso) (62J07)

Related Items (4)

A hierarchical Bayesian perspective on majorization-minimization for non-convex sparse regression: application to M/EEG source imaging ⋮ Robust censored regression with \(\ell_1\)-norm regularization ⋮ High-dimensional inference robust to outliers with ℓ1-norm penalization ⋮ Inference robust to outliers with ℓ₁-norm penalization

Cites Work

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• \(\ell_{1}\)-penalization for mixture regression models
• The restricted isometry property and its implications for compressed sensing
• Robust estimation for an inverse problem arising in multiview geometry
• Simultaneous analysis of Lasso and Dantzig selector
• The Dantzig selector: statistical estimation when \(p\) is much larger than \(n\). (With discussions and rejoinder).
• Penalized regression, standard errors, and Bayesian Lassos
• High-dimensional regression with unknown variance

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