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Outlier detection based on extreme value theory and applications

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  • Shrijita Bhattacharya
  • Francois Kamper
  • Jan Beirlant

Abstract

Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behavior of the underlying distribution. We develop an automatic, data‐driven method rooted in the mathematical theory of extremes to identify observations that deviate from the intermediate and central characteristics. The proposed algorithm is an extension of a method previously proposed in the literature for the specific case of heavy tailed Pareto‐type distributions to all max‐domains of attraction. We propose some applications such as a tail‐adjusted boxplot which yields a more accurate representation of possible outliers, and the identification of outliers in a multivariate context through an analysis of associated random variables such as local outlier factors. Several examples and simulation results illustrate the finite sample behavior of the algorithm and its applications.

Suggested Citation

  • Shrijita Bhattacharya & Francois Kamper & Jan Beirlant, 2023. "Outlier detection based on extreme value theory and applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 50(3), pages 1466-1502, September.
    • Handle: RePEc:bla:scjsta:v:50:y:2023:i:3:p:1466-1502
    DOI: 10.1111/sjos.12665
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    References listed on IDEAS

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    1. Vandewalle, B. & Beirlant, J. & Christmann, A. & Hubert, M., 2007. "A robust estimator for the tail index of Pareto-type distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(12), pages 6252-6268, August.
    2. Hubert, M. & Vandervieren, E., 2008. "An adjusted boxplot for skewed distributions," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5186-5201, August.
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