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Cellwise robust M regression

Author

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  • Filzmoser, P.
  • Höppner, S.
  • Ortner, I.
  • Serneels, S.
  • Verdonck, T.

Abstract

The cellwise robust M regression estimator is introduced as the first estimator of its kind that intrinsically yields both a map of cellwise outliers consistent with the linear model, and a vector of regression coefficients that is robust against vertical outliers and leverage points. As a by-product, the method yields a weighted and imputed data set that contains estimates of what the values in cellwise outliers would need to amount to if they had fit the model. The method is illustrated to be equally robust as its casewise counterpart, MM regression. The cellwise regression method discards less information than any casewise robust estimator. Therefore, predictive power can be expected to be at least as good as casewise alternatives. These results are corroborated in a simulation study. Moreover, while the simulations show that predictive performance is at least on par with casewise methods if not better, an application to a data set consisting of compositions of Swiss nutrients, shows that in individual cases, CRM can achieve a much higher predictive accuracy compared to MM regression.

Suggested Citation

  • Filzmoser, P. & Höppner, S. & Ortner, I. & Serneels, S. & Verdonck, T., 2020. "Cellwise robust M regression," Computational Statistics & Data Analysis, Elsevier, vol. 147(C).
    • Handle: RePEc:eee:csdana:v:147:y:2020:i:c:s0167947320300359
    DOI: 10.1016/j.csda.2020.106944
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    References listed on IDEAS

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    1. Heinrich Fritz & Peter Filzmoser & Christophe Croux, 2012. "A comparison of algorithms for the multivariate L 1 -median," Computational Statistics, Springer, vol. 27(3), pages 393-410, September.
    2. Matías Salibián-Barrera & Stefan Aelst & Gert Willems, 2008. "Fast and robust bootstrap," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 17(1), pages 41-71, February.
    3. Koller, Manuel & Stahel, Werner A., 2011. "Sharpening Wald-type inference in robust regression for small samples," Computational Statistics & Data Analysis, Elsevier, vol. 55(8), pages 2504-2515, August.
    4. Peter Leoni & Pieter Segaert & Sven Serneels & Tim Verdonck, 2018. "Multivariate constrained robust M‐regression for shaping forward curves in electricity markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 38(11), pages 1391-1406, November.
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    Cited by:

    1. Nikola Štefelová & Andreas Alfons & Javier Palarea-Albaladejo & Peter Filzmoser & Karel Hron, 2021. "Robust regression with compositional covariates including cellwise outliers," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 15(4), pages 869-909, December.

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