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

Author

Listed:
  • Jaromír Antoch

    (Charles University
    Prague University of Economics and Business)

  • Michal Černý

    (Prague University of Economics and Business)

  • Ryozo Miura

    (Tohoku University)

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.

Suggested Citation

  • Jaromír Antoch & Michal Černý & Ryozo Miura, 2025. "R-estimation in linear models: algorithms, complexity, challenges," Computational Statistics, Springer, vol. 40(1), pages 405-439, January.
    • Handle: RePEc:spr:compst:v:40:y:2025:i:1:d:10.1007_s00180-024-01495-0
    DOI: 10.1007/s00180-024-01495-0
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    References listed on IDEAS

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