Antipodal Reflection Depth (ARD) and Its Application to Nonparametric Outlier Detection in Multivariate and Functional Data

• Activity Number: 66
• Type: Topic Contributed
• Date/Time: Sunday, August 9, 2015 : 4:00 PM to 5:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Yi Fan* and Regina Y. Liu
• Companies: Rutgers University and Rutgers University
• Keywords: data depth ; functional data analysis ; outlier detection

Abstract

Data depth, as a measure of centrality and center-outward ordering, has been developed into a powerful nonparametric alternative to the analysis of multivariate or functional data. We introduce a general approach, called antipodal reflection depth (ARD), to refine any existing data depth (referred to as the base depth) to yield a class of new data depths. This approach is completely data driven and nonparametric. ARD combines antipodal reflections of original sample in the calculation of depth values but draws inferences using only the original sample with their ARD depth values. ARD can i) preserve the deepest point and the center-outward ordering along each ray from this deepest point obtained by the base depth; and ii) capture the relative magnitudes of deviation from sample points to the deepest point. Property ii) is generally lacking in the existing data depths due to their location-scale free nature. ARD can provide an effective approach for outlier detection in both multivariate and functional data. Besides simulation studies, ARD is also applied to identify possible anomalous aircraft landings.