Nonparametric Outlier Detection with Functional Data Using the Spatial Depth Approach

• Activity Number: 383
• Type: Topic Contributed
• Date/Time: Tuesday, August 5, 2014 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Uditha Wijesuriya*+ and Robert Serfling
• Companies: University of Texas at Dallas and University of Texas at Dallas
• Keywords: functional data ; nonparametric ; outlier detection ; multivariate ; spatial depth

Abstract

The spatial depth and outlyingness approach with multivariate data has been very successful for its tractability, computational ease, and convenient asymptotics. Here its extension to the setting of outlier identification in functional data analysis is treated. Computations may be carried out in the Hilbert space of curves or in a corresponding Euclidean space obtained by discretization. For a data set of real-valued curves, methods are described for useful display of the sample median curve, the 50% central region of curves, and sample "outlier" curves, including both location and shape outliers. A spatial functional boxplot approach is used to identify outliers. Here we illustrate with several actual and simulated data sets, comparing the spatial approach with several leading competing methods, with respect to the false positive rate, the false negative rate, and the computational burden as criteria. It is seen that the spatial approach is among the very best in performance.