论文标题
基于订单统计比率的离群值概念
On a Notion of Outliers Based on Ratios of Order Statistics
论文作者
论文摘要
统计中“离群值”一词的数学形式主义有许多数学形式主义，尽管对正确的概念尚无共识。因此，我们试图为通过订单统计定义的特定类型的异常值提供一个一致且可靠的定义。我们的方法是基于订单统计的部分总和的比率，以研究假设和经验分布的尾巴行为。我们在一组分布上模拟我们的统计量，以标记潜在异常值，并使用算法自动选择一个截止点，而无需任何其他先验假设。最后，我们通过对莱维稳定区域以外的两个帕累托尾部区分统计量的统计数据的功效。
There are a number of mathematical formalisms of the term "outlier" in statistics, though there is no consensus on what the right notion ought to be. Accordingly, we try to give a consistent and robust definition for a specific type of outliers defined via order statistics. Our approach is based on ratios of partial sums of order statistics to investigate the tail behaviors of hypothetical and empirical distributions. We simulate our statistic on a set of distributions to mark potential outliers and use an algorithm to automatically select a cut-off point without the need of any further a priori assumption. Finally, we show the efficacy of our statistic by a simulation study on distinguishing two Pareto tails outside of the Lévy stable region.
