Masking and Swamping Robustness of Leading Nonparametric Outlier Identifiers for Multivariate Data

• Activity Number: 505
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Shanshan Wang*+ and Robert Serfling
• Companies: and University of Texas at Dallas
• Keywords: Masking robustness ; Swamping robustness ; Breakdown point ; Nonparametric ; Multivariate ; Outlier detection

Abstract

Two key measures for studying robustness of outlier detection procedures are breakdown points associated with masking and swamping, respectively. Here masking and swamping breakdown points are evaluated and compared for three leading outlier identifiers in the setting of multivariate data: Mahalanobis distance outlyingness, spatial outlyingness, and projection outlyingness. For Mahalanobis distance outlyingness, we consider several examples of location and scatter estimators, including the classical estimators and the robust, but computationally intensive, Minimum Covariance Determinant (MCD) estimators. The spatial outlyingness extends its univariate counterpart, centered rank outlyingness. For projection outlyingness, which extends univariate scaled deviation outlyingness, we consider several variations, including M-estimators for location and scale, as well as the median and modified MAD.