Each week, we select a recently published Open Access article to feature. This week’s article comes from the Scandinavian Journal of Statistics and develops a method to identify observations that deviate from the intermediate and central characteristics. 

The article’s abstract is given below, with the full article available to read here.  

Bhattacharya, S., Kamper, F., & Beirlant, J. (2023). Outlier detection based on extreme value theory and applications. Scand J Statist, 1– 37. https://doi.org/10.1111/sjos.12665

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.