The place of the \(L_ 1\)-norm in robust estimation

DOI10.1016/0167-9473(87)90049-1zbMath0623.62025OpenAlexW1562577836MaRDI QIDQ1091694

Peter J. Huber

Publication date: 1987

Published in: Computational Statistics and Data Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0167-9473(87)90049-1

zbMATH Keywords

sensitivityoutliersM-estimatesbreakdown pointrobust estimationregression diagnosticsmultiple regressioniterative proceduresinfluential points\(L_ 1\)-estimationchoice of weightsconstant weightsgeneralization of sample medianHampel- Krasker-Welsch-type weightslocal shiftsminimal biasminimax asymptotic bias

Mathematics Subject Classification ID

Asymptotic properties of parametric estimators (62F12) Linear regression; mixed models (62J05) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items (7)

Least absolute deviations estimation for uncertain regression with imprecise observations ⋮ Accelerated sparse recovery via gradient descent with nonlinear conjugate gradient momentum ⋮ On sparsity‐inducing methods in system identification and state estimation ⋮ Optimization approaches to supervised classification ⋮ Least absolute value regression: recent contributions ⋮ Permutation tests using least distance estimator in the multivariate regression model ⋮ Analysis of a nonsmooth optimization approach to robust estimation

Cites Work

• Robust regression: Asymptotics, conjectures and Monte Carlo
• Least Median of Squares Regression
• Minimax Aspects of Bounded-Influence Regression
• Robust regression using repeated medians
• Robust Statistics
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