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Benchmark testing of algorithms for very robust regression: FS, LMS and LTS

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  • Torti, Francesca
  • Perrotta, Domenico
  • Atkinson, Anthony C.
  • Riani, Marco

Abstract

The methods of very robust regression resist up to 50% of outliers. The algorithms for very robust regression rely on selecting numerous subsamples of the data. New algorithms for LMS and LTS estimators that have increased computational efficiency due to improved combinatorial sampling are proposed. These and other publicly available algorithms are compared for outlier detection. Timings and estimator quality are also considered. An algorithm using the forward search (FS) has the best properties for both size and power of the outlier tests.

Suggested Citation

  • Torti, Francesca & Perrotta, Domenico & Atkinson, Anthony C. & Riani, Marco, 2012. "Benchmark testing of algorithms for very robust regression: FS, LMS and LTS," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2501-2512.
    • Handle: RePEc:eee:csdana:v:56:y:2012:i:8:p:2501-2512
    DOI: 10.1016/j.csda.2012.02.003
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    References listed on IDEAS

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    1. Marco Riani & Anthony C. Atkinson & Andrea Cerioli, 2009. "Finding an unknown number of multivariate outliers," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(2), pages 447-466, April.
    2. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
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    Citations

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    Cited by:

    1. Flores, Salvador, 2015. "SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression," European Journal of Operational Research, Elsevier, vol. 246(1), pages 44-50.
    2. Selin Ahipaşaoğlu, 2015. "Fast algorithms for the minimum volume estimator," Journal of Global Optimization, Springer, vol. 62(2), pages 351-370, June.
    3. Eugster, Manuel J.A. & Leisch, Friedrich & Strobl, Carolin, 2014. "(Psycho-)analysis of benchmark experiments: A formal framework for investigating the relationship between data sets and learning algorithms," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 986-1000.
    4. Christian Garciga & Randal J. Verbrugge, 2020. "A New Tool for Robust Estimation and Identification of Unusual Data Points," Working Papers 20-08, Federal Reserve Bank of Cleveland.
    5. Garciga, Christian & Verbrugge, Randal, 2021. "Robust covariance matrix estimation and identification of unusual data points: New tools," Research in Economics, Elsevier, vol. 75(2), pages 176-202.
    6. Arismendi, Juan C. & Broda, Simon, 2017. "Multivariate elliptical truncated moments," Journal of Multivariate Analysis, Elsevier, vol. 157(C), pages 29-44.
    7. Baishuai Zuo & Chuancun Yin, 2022. "Multivariate doubly truncated moments for generalized skew-elliptical distributions with application to multivariate tail conditional risk measures," Papers 2203.00839, arXiv.org.
    8. Greco, Luca & Pacillo, Simona & Maresca, Piera, 2023. "An impartial trimming algorithm for robust circle fitting," Computational Statistics & Data Analysis, Elsevier, vol. 181(C).
    9. Baishuai Zuo & Chuancun Yin & Jing Yao, 2023. "Multivariate range Value-at-Risk and covariance risk measures for elliptical and log-elliptical distributions," Papers 2305.09097, arXiv.org.
    10. Maria Teresa Alonso & Carlo Ferigato & Deimos Ibanez Segura & Domenico Perrotta & Adria Rovira-Garcia & Emmanuele Sordini, 2021. "Analysis of ‘Pre-Fit’ Datasets of gLAB by Robust Statistical Techniques," Stats, MDPI, vol. 4(2), pages 1-19, May.
    11. Mount, David M. & Netanyahu, Nathan S. & Piatko, Christine D. & Wu, Angela Y. & Silverman, Ruth, 2016. "A practical approximation algorithm for the LTS estimator," Computational Statistics & Data Analysis, Elsevier, vol. 99(C), pages 148-170.

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