Outlier detection based on extreme value theory and applications

Whether an extreme observation is an outlier or not depends strongly on the corresponding tail behaviour 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 a generalization of the method proposed in Bhattacharya et al. (2019) for the specific case of heavy tailed Pareto-type distributions to all max-domains of attraction. Consequently 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 the analysis of outliers of associated random variables such as density estimates. Several examples and simulation results illustrate the finite sample behaviour of the algorithm.