Maximum bias curves for robust regression with non-elliptical regressors

DOI10.1214/aos/996986507zbMath1029.62028OpenAlexW1971762149MaRDI QIDQ1848860

Ruben H. Zamar, José R. Berrendero

Publication date: 14 November 2002

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

Full work available at URL: https://doi.org/10.1214/aos/996986507

zbMATH Keywords

S-estimatesR-estimatestau-estimatesmaxbias curve

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Robustness and adaptive procedures (parametric inference) (62F35)

Related Items

The maximum asymptotic bias of S-estimates for regression over the neighborhoods defined by certain special capacities ⋮ Robust tests for linear regression models based on \(\tau\)-estimates ⋮ APPLIED REGRESSION ANALYSIS BIBLIOGRAPHY UPDATE 2000–2001 ⋮ Efficient Robust Regression via Two-Stage Generalized Empirical Likelihood ⋮ Robust and efficient estimation of the residual scale in linear regression ⋮ High-breakdown robust multivariate methods ⋮ Globally robust inference for the location and simple linear regression models ⋮ Bias robustness of three median-based regression estimates. ⋮ On the maximum bias functions of \(MM\)-estimates and constrained \(M\)-estimates of regression ⋮ Bias bound for the minimax estimator ⋮ Empirical analysis of the maximum asymptotic bias of location estimators for fuzzy number-valued data ⋮ A parametric framework for the comparison of methods of very robust regression

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Bias-robust estimates of regression based on projections
• Bias robust estimation of scale
• Min-max bias robust regression
• A local breakdown property of robust tests in linear regression
• On the optimality of S-estimators
• Bias robust estimation in orthogonal regression
• Stability under contamination of robust regression estimators based on differences of residuals.
• Minimax bias-robust estimation of the dispersion matrix of a multivariate distribution
• A minimax-bias property of the least \(\alpha\)-quantile estimates
• Asymptotics of generalized \(S\)-estimators
• Optimal locally robust M-estimates of regression
• Globally robust inference for the location and simple linear regression models
• Functional stability of one-step GM-estimators in approximately linear regression
• The ``automatic robustness of minimum distance functionals
• Positive-breakdown regression by minimizing nested scale estimators
• Lower bounds for contamination bias: Globally minimax versus locally linear estimation
• Least Median of Squares Regression
• Projection-Pursuit Approach to Robust Dispersion Matrices and Principal Components: Primary Theory and Monte Carlo
• High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale
• On One-Step GM Estimates and Stability of Inferences in Linear Regression
• Rank-Based Estimates in the Linear Model with High Breakdown Point
• Regression Depth
• Robust Estimation of a Location Parameter
• Robust Statistics