JSM 2005 - Toronto

Abstract #303042

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Legend: = Applied Session, = Theme Session, = Presenter
Activity Number: 103
Type: Contributed
Date/Time: Monday, August 8, 2005 : 8:30 AM to 10:20 AM
Sponsor: IMS
Abstract - #303042
Title: Nonparametric Depth-Based Multivariate Outlier Identifiers and Robustness Properties
Author(s): Xin Dang*+ and Robert Serfling
Companies: The University of Texas Southwestern Medical Center at Dallas and The University of Texas Southwestern Medical Center at Dallas
Address: Mathematical Science Dept, Richardson, TX, 75083, United States
Keywords: outliers ; nonparametric ; multivariate ; robustness ; breakdown points ; influence functions
Abstract:

A new approach for multivariate outlier detection, which is nonparametric in character and based on statistical depth functions, is formulated. It competes, for example, with popular methods based on the Mahalanobis distance, which imposes elliptical outlyingness contours. To study robustness of these nonparametric outlier identifiers, notions of masking and swamping breakdown point are formulated, and general properties are derived under natural assumptions on the depth function. An interesting feature, for example, is that such outlier identifiers are able to handle the masking effects of extreme outliers more easily than those of less extreme ones, in contrast with the robustness of statistical estimators, which perform worse in the presence of more extreme outliers. Further, an influence function analysis is developed. Using masking and swamping breakdown points and influence functions, outlier identification methods based on the halfspace, simplicial, spatial, and projection depth functions are characterized and compared.

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