Cellwise Robust M Regression

TL;DR

This paper introduces a novel cellwise robust M regression estimator that identifies cellwise outliers, provides robust regression coefficients, and maintains high predictive accuracy, outperforming traditional casewise methods in some cases.

Contribution

The paper presents the first cellwise robust M regression estimator that detects cellwise outliers and offers robust coefficients while preserving predictive power.

Findings

Estimator effectively identifies cellwise outliers.

Comparable or superior predictive performance to casewise methods.

Application shows significant accuracy improvements in real data.

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.