Robust Detection of Multiple Outliers in Grouped Multivariate Data

• Activity Number: 54
• Type: Contributed
• Date/Time: Sunday, August 8, 2004 : 4:00 PM to 5:50 PM
• Sponsor: General Methodology
• Author(s): Nedret Billor*+ and Chrys Caroni
• Companies: Auburn University and National Technical University of Athens
• Keywords: multivariate data ; outliers ; robust methods ; cluster analysis

Abstract

Many methods have been developed for detecting multiple outliers in a single multivariate sample, but very little on the case where there may be groups on the data. We propose a method of simultaneously determining groups (as in cluster analysis) and detecting outliers, which are points that are distant from every group. Our method is an adaptation of the BACON algorithm proposed by Billor, Hadi, and Velleman for the robust detection of multiple outliers in a single group of multivariate data. There are two versions of our method, depending on whether or not the groups can be assumed to have equal covariance matrices. The effectiveness of the method is shown by a simulation study for different sample sizes and dimensions for two and three groups, with and without planted outliers in the data. When the number of groups is not known in advance, the algorithm could be used as a robust method of cluster analysis, by running it for various numbers of groups and choosing the best solution.