R-estimation in linear models: algorithms, complexity, challenges

Jaromír Antoch (), Michal Černý () and Ryozo Miura ()
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Jaromír Antoch: Charles University
Michal Černý: Prague University of Economics and Business
Ryozo Miura: Tohoku University

Computational Statistics, 2025, vol. 40, issue 1, No 17, 405-439

Abstract: Abstract The main objective of this paper is to discuss selected computational aspects of robust estimation in the linear model with the emphasis on R-estimators. We focus on numerical algorithms and computational efficiency rather than on statistical properties. In addition, we formulate some algorithmic properties that a “good” method for R-estimators is expected to satisfy and show how to satisfy them using the currently available algorithms. We illustrate both good and bad properties of the existing algorithms. We propose two-stage methods to minimize the effect of the bad properties. Finally we justify a challenge for new approaches based on interior-point methods in optimization.

Keywords: Linear regression model; R-estimators; Least squares estimator; $$L_1$$ L 1 -norm estimator; Iteratively reweighted least squares; Iterated weighted least squares; s-step R-estimators; Newton-like algorithm; Line and simplex search; Discrete and continuous optimization; Arrangement of hyperplanes (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s00180-024-01495-0

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