Breakdown points and variation exponents of robust \(M\)-estimators in linear models

DOI10.1214/aos/1017938920zbMath0959.62029OpenAlexW2064534526MaRDI QIDQ1568279

Christine H. Müller, Ivan Mizera

Publication date: 2 May 2001

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/aos/1017938920

zbMATH Keywords

regular variationlinear modelbreakdown pointM-estimatorL1 estimator

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Design of statistical experiments (62K99) Point estimation (62F10) Robustness and adaptive procedures (parametric inference) (62F35) Analysis of variance and covariance (ANOVA) (62J10)

Related Items (14)

Tail behavior of the least-squares estimator ⋮ Breakdown points of Cauchy regression-scale estimators ⋮ Robustness and Tractability for Non-convex M-estimators ⋮ Sharp non-asymptotic performance bounds for \(\ell_1\) and Huber robust regression estimators ⋮ Data depth for simple orthogonal regression with application to crack orientation ⋮ Ultrahigh dimensional variable selection through the penalized maximum trimmed likelihood estimator ⋮ A constrained-optimization based half-quadratic algorithm for robustly Fitting sets of linearly parametrized curves ⋮ Robust signal extraction for on-line monitoring data. ⋮ Non-Gaussian quasi-likelihood estimation of SDE driven by locally stable Lévy process ⋮ Explaining the seismic moment of large earthquakes by heavy and extremely heavy tailed models ⋮ Outlier robust corner-preserving methods for reconstructing noisy images ⋮ A Revisited Half-Quadratic Approach for Simultaneous Robust Fitting of Multiple Curves ⋮ Galton, Edgeworth, Frisch, and prospects for quantile regression in econometrics ⋮ Asymptotic and Finite-Sample Properties in Statistical Estimation

Cites Work

• Finite sample breakdown of M- and P-estimators
• Tail-behavior of location estimators
• Robust estimation in structured linear regression
• Robust planning and analysis of experiments
• Breakdown points for designed experiments
• On the unimodality of the likelihood for the Cauchy distribution: Some comments
• Tail Behavior of Regression Estimators and their Breakdown Points
• Leverage and Breakdown in L 1 Regression
• On the unimodality of the likelihood for the Cauchy distribution
• Robust Statistics
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