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

Listed author(s):
  • Torti, Francesca
  • Perrotta, Domenico
  • Atkinson, Anthony C.
  • Riani, Marco

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.

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Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

Volume (Year): 56 (2012)
Issue (Month): 8 ()
Pages: 2501-2512

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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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  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.
  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.
  3. Nunkesser, Robin & Morell, Oliver, 2010. "An evolutionary algorithm for robust regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3242-3248, December.
  4. Atkinson, A.C. & Riani, M., 2007. "Exploratory tools for clustering multivariate data," Computational Statistics & Data Analysis, Elsevier, vol. 52(1), pages 272-285, September.
  5. Flores, Salvador, 2010. "On the efficient computation of robust regression estimators," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3044-3056, December.
  6. Mastronardi, Nicola & O'Leary, Dianne P., 2007. "Fast robust regression algorithms for problems with Toeplitz structure," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 1119-1131, October.
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