Robust three-step regression based on comedian and its performance in cellwise and casewise outliers

Abstract

Cellwise and casewise outliers may appear both at the same time in real data. Few methods have developed statistical methods to deal both types of outliers in regression models. We propose a new three-step regression method that uses the comedian as highly robust scatter estimate in a known threestep regression (3S-regression). The procedure introduced here, shows in general, an outperformance respect to recent robust methods. We test the comedian three-step regression (C3S-regression) in both synthetic and real data. The results of this paper show that the proposed C3S-regression is highly robust in presence of cellwise and casewise outliers. We also extend the results to models with continuous and dummy covariates.