Robust Regression for Handling Cell-Wise and Case-Wise Contamination

• Activity Number: 318
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Andrew Leung* and Hongyang Zhang and Ruben Zamar
• Companies: The University of British Columbia and The University of British Columbia and The University of British Columbia
• Keywords: robustness ; regression ; cellwise outliers ; componentwise contamination ; S-estimator

Abstract

Traditional robust regression methods may fail when data contains cell-wise outliers. Cell-wise outliers are likely to occur together with case-wise outliers in modern datasets. The proposed method, called 3S-regression, proceeds as follows: first it uses a univariate filter to detect and eliminate extreme cell-wise outliers; second it applies a robust estimator of multivariate location and scatter to the filtered data to down-weight case-wise outliers; third it computes robust regression coefficients from the estimates obtained in the second step. The estimator is consistent and asymptotically normal at the central model under mild assumptions on the tail distributions of the predictors. Extensive simulation results show that 3S-regression is resilient to cell-wise outliers. It also performs well under case-wise contaminations when comparing with traditional high breakdown point estimators.