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Robust Detection of Multiple Outliers in Grouped Multivariate Data

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  • Chrys Caroni
  • Nedret Billor

Abstract

Many methods have been developed for detecting multiple outliers in a single multivariate sample, but very few for the case where there may be groups in 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 illustrated by its application to two real data sets and further shown by a simulation study for different sample sizes and dimensions for 2 and 3 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.

Suggested Citation

  • Chrys Caroni & Nedret Billor, 2007. "Robust Detection of Multiple Outliers in Grouped Multivariate Data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 34(10), pages 1241-1250.
    • Handle: RePEc:taf:japsta:v:34:y:2007:i:10:p:1241-1250
    DOI: 10.1080/02664760701592877
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    References listed on IDEAS

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    1. N. A. Campbell, 1980. "Robust Procedures in Multivariate Analysis I: Robust Covariance Estimation," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(3), pages 231-237, November.
    2. Billor, Nedret & Hadi, Ali S. & Velleman, Paul F., 2000. "BACON: blocked adaptive computationally efficient outlier nominators," Computational Statistics & Data Analysis, Elsevier, vol. 34(3), pages 279-298, September.
    3. M. J. Baxter, 1995. "Standardization and Transformation in Principal Component Analysis, with Applications to Archaeometry," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 44(4), pages 513-527, December.
    4. Hardin, Johanna & Rocke, David M., 2004. "Outlier detection in the multiple cluster setting using the minimum covariance determinant estimator," Computational Statistics & Data Analysis, Elsevier, vol. 44(4), pages 625-638, January.
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