Bhattacharya, ShrijitaKamper, FrancoisBeirlant, Jan2023-06-052023-06-052023-06-052023-05-2110.1111/sjos.12665https://infoscience.epfl.ch/handle/20.500.14299/198084WOS:000990219100001Whether 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.Statistics & ProbabilityMathematicsextreme observationslocal outlier factorsmajority vote plotmax-domain of attractiontail-adjusted boxplotestimatorindextailtext::journal::journal article::research article