High-Dimensional Outliers and Depth: The Outliergram

• Activity Number: 674
• Type: Topic Contributed
• Date/Time: Thursday, August 13, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Juan Romo* and Ana Arribas-Gil
• Companies: Universidad Carlos III de Madrid and Universidad Carlos III de Madrid
• Keywords: High-dimensional data ; Depth ; Outliers ; Outliergram

Abstract

An important question when analyzing functional data is detecting shape outliers. Given a sample of curves, shape outliers can be defined as those curves presenting a different shape from the rest of the sample. These outlying curves may not take atypical values and thus be masked among the rest of the curves, which makes them difficult to detect. Our method relies on the combination of two depth measures for functional data whose relationship is investigated. A 2D-plot of one of these measures against the other results in a graphic in which points corresponding to shape outliers lie far away from the majority of the data. The use of this visualization tool, the outliergram, is illustrated through several examples. Moreover, we present an algorithm for shape outlier detection and analyze its performance.