Sharp non-asymptotic performance bounds for \(\ell_1\) and Huber robust regression estimators

DOI10.1007/s11749-015-0435-5zbMath1329.62311OpenAlexW2044101683MaRDI QIDQ905107

Salvador Flores

Publication date: 14 January 2016

Published in: Test (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11749-015-0435-5

zbMATH Keywords

breakdown point\(\ell_1\) norm minimizationHuber M-estimatorleverage constantsleverage plotsparse outliers

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Robustness and adaptive procedures (parametric inference) (62F35) Sensitivity, stability, parametric optimization (90C31)

Cites Work

• Unnamed Item
• Unnamed Item
• Theory of compressive sensing via \(\ell_1\)-minimization: a non-RIP analysis and extensions
• Robust weighted LAD regression
• Duality results and proximal solutions of the Huber \(M\)-estimator problem
• Instability of least squares, least absolute deviation and least median of squares linear regression. (With a comment and a rejoinder).
• Breakdown points and variation exponents of robust \(M\)-estimators in linear models
• Alternative methods of linear regression
• Robust regression: Asymptotics, conjectures and Monte Carlo
• Decoding by Linear Programming
• Highly Robust Error Correction byConvex Programming
• Tail Behavior of Regression Estimators and their Breakdown Points
• Leverage and Breakdown in L 1 Regression
• The Finite Sample Breakdown Point of \boldmath$\ell_1$-Regression
• A mathematical programming approach for improving the robustness of least sum of absolute deviations regression
• Signal Recovery by Proximal Forward-Backward Splitting

This page was built for publication: Sharp non-asymptotic performance bounds for \(\ell_1\) and Huber robust regression estimators