Robust Three-Step Regression Based on Comedian and Its Performance in Cell-Wise and Case-Wise Outliers

• Main Authors: Henry Velasco, Henry Laniado, Mauricio Toro, Víctor Leiva, Yuhlong Lio
• Format: Article
• Language: English
• Published: MDPI AG 2020-08-01
• Series: Mathematics
• Subjects: case-wise contamination; comedian; MAD; Monte Carlo simulation; R software; robustness
• Online Access: https://www.mdpi.com/2227-7390/8/8/1259

Both cell-wise and case-wise outliers may appear in a real data set at the same time. Few methods have been developed in order to deal with both types of outliers when formulating a regression model. In this work, a robust estimator is proposed based on a three-step method named 3S-regression, which uses the comedian as a highly robust scatter estimate. An intensive simulation study is conducted in order to evaluate the performance of the proposed comedian 3S-regression estimator in the presence of cell-wise and case-wise outliers. In addition, a comparison of this estimator with recently developed robust methods is carried out. The proposed method is also extended to the model with continuous and dummy covariates. Finally, a real data set is analyzed for illustration in order to show potential applications.