Least quantile regression via modern optimization

DOI10.1214/14-AOS1223zbMath1302.62154arXiv1310.8625MaRDI QIDQ482902

Rahul Mazumder, Dimitris J. Bertsimas

Publication date: 6 January 2015

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

Full work available at URL: https://arxiv.org/abs/1310.8625

zbMATH Keywords

algorithmsglobal optimizationmixed integer programmingrobust statisticscontinuous optimizationleast median of squaresleast quantile regression

Mathematics Subject Classification ID

Nonparametric robustness (62G35) Linear regression; mixed models (62J05) Mixed integer programming (90C11) Nonconvex programming, global optimization (90C26)

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Uses Software

• Gurobi
• robustbase
• rrcov
• PROGRESS

Cites Work

• The feasible set algorithm for least median of squares regression
• An approximation algorithm for least median of squares regression
• On the least median square problem
• High-breakdown robust multivariate methods
• Least median of squares and regression through the origin
• A practical approximation algorithm for the LMS line estimator
• Algorithms and complexity for least median of squares regression
• Introductory lectures on convex optimization. A basic course.
• Robust regression: Asymptotics, conjectures and Monte Carlo
• Least trimmed squares regression, least median squares regression, and mathematical program\-ming
• An evolutionary algorithm for robust regression
• QUANTILE APPROXIMATION FOR ROBUST STATISTICAL ESTIMATION AND k-ENCLOSING PROBLEMS
• Least Median of Squares Regression
• Time- and Space-Efficient Algorithms for Least Median of Squares Regression
• Robust regression using repeated medians
• One-Step Huber Estimates in the Linear Model
• Computing the Exact Least Median of Squares Estimate and Stability Diagnostics in Multiple Linear Regression
• Robust Parameter Estimation in Computer Vision
• Convex Analysis
• A General Qualitative Definition of Robustness
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