Instability of least squares, least absolute deviation and least median of squares linear regression. (With a comment and a rejoinder).

DOI10.1214/ss/1028905829zbMath1059.62558OpenAlexW1972125098MaRDI QIDQ1431151

Steven P. Ellis

Publication date: 27 May 2004

Published in: Statistical Science (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1214/ss/1028905829

zbMATH Keywords

stabilitysingularityCollinearity

Mathematics Subject Classification ID

Linear regression; mixed models (62J05) Diagnostics, and linear inference and regression (62J20)

Related Items (8)

On adaptive linear regression ⋮ Sharp non-asymptotic performance bounds for \(\ell_1\) and Huber robust regression estimators ⋮ Instability of least squares, least absolute deviation and least median of squares linear regression. (With a comment and a rejoinder). ⋮ Sensitivity analysis of constrained linear \(L_1\) regression: perturbations to response and predictor variables ⋮ Least absolute value regression: recent contributions ⋮ Sensitivity analysis of constrained linear \(L_1\) regression: Perturbations to constraints, addition and deletion of observations ⋮ Bayesian outlier detection in Capital Asset Pricing Model ⋮ Novel global harmony search algorithm for least absolute deviation

Uses Software

• R
• S-PLUS
• bootstrap

Cites Work

• The singularities of fitting planes to data
• Exactly what is being modelled by the systematic component in a heteroscedastic linear regression
• Aspects of robust linear regression
• Unconventional features of positive-breakdown estimators
• Instability of least squares, least absolute deviation and least median of squares linear regression. (With a comment and a rejoinder).
• Direct use of regression quantiles to construct confidence sets in linear models
• Least Median of Squares Regression
• Saddlepoint approximations for regression models
• Leverage and Breakdown in L 1 Regression
• Statistical inference on heteroscedastic models based on regression quantiles
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