Outlier detection based on extreme value theory and applications
提出一种基于极值理论的自动数据驱动方法，用于识别偏离中间和中心特征的观测值，并应用于调整箱线图和多元异常值检测。
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.