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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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    1. Milan Hladík & Michal Černý & Jaromír Antoch, 2020. "EIV regression with bounded errors in data: total ‘least squares’ with Chebyshev norm," Statistical Papers, Springer, vol. 61(1), pages 279-301, February.
    2. Marc Hallin & Davy Paindaveine & Thomas Verdebout, 2014. "Efficient R-Estimation of Principal and Common Principal Components," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(507), pages 1071-1083, September.
    3. Hallin, Marc & Swan, Yvik & Verdebout, Thomas & Veredas, David, 2013. "One-step R-estimation in linear models with stable errors," Journal of Econometrics, Elsevier, vol. 172(2), pages 195-204.
    4. Fuchang Gao & Lixing Han, 2012. "Implementing the Nelder-Mead simplex algorithm with adaptive parameters," Computational Optimization and Applications, Springer, vol. 51(1), pages 259-277, January.
    5. A. Saleh & Jan Picek & Jan Kalina, 2012. "R-estimation of the parameters of a multiple regression model with measurement errors," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(3), pages 311-328, April.
    6. Marc Hallin & Chintan Mehta, 2015. "R -Estimation for Asymmetric Independent Component Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 218-232, March.
    7. Hallin, Marc & La Vecchia, Davide, 2017. "R-estimation in semiparametric dynamic location-scale models," Journal of Econometrics, Elsevier, vol. 196(2), pages 233-247.
    8. Antoch, Jaromir & Ekblom, Hakan, 1995. "Recursive robust regression computational aspects and comparison," Computational Statistics & Data Analysis, Elsevier, vol. 19(2), pages 115-128, February.
    9. Delphine Cassart & Marc Hallin & Davy Paindaveine, 2010. "On the estimation of cross-information quantities in rank-based inference," Working Papers ECARES ECARES 2010-010, ULB -- Universite Libre de Bruxelles.
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