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Cellwise Robust M Regression
Methodology · Submitted 7 Dec 2019
abstract compiled · 2026-09-23 · no language-model review
The authors' main claim 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 significantly higher predictive accuracy compared to MM regression.
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The abstract, sentence by sentence
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 significantly higher predictive accuracy compared to MM regression.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | 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. | contribution 1.00 | 0.89 | 0.41 | asserted 1.00 |
| s1 | 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. | result 0.60 | 0.89 | 0.05 | asserted 1.00 |
| s2 | The method is illustrated to be equally robust as its casewise counterpart, MM regression. | result 1.00 | 0.82 | 0.13 | asserted 1.00 |
| s3 | The cellwise regression method discards less information than any casewise robust estimator. | result 0.78 | 0.73 | 0.19 | asserted 1.00 |
| s4 | Therefore, predictive power can be expected to be at least as good as casewise alternatives. | interpretation 0.99 | 0.35 | 0.18 | hedged possibility 0.97 |
| s5 | These results are corroborated in a simulation study. | result 0.81 | 0.87 | 0.07 | asserted 0.99 |
| s6 | 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 significantly higher predictive accuracy compared to MM regression. | result 1.00 | 0.95 | 0.28 | asserted 0.94 |
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The paper
Original 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 significantly higher predictive accuracy compared to MM regression.
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