Multiple Outlier Detection in Samples with Exponential & Pareto Tails: Redeeming the Inward Approach & Detecting Dragon Kings

TL;DR

This paper introduces robust ratio-based tests for outlier detection in heavy-tailed data, revalidates inward testing, and applies these methods to identify significant outliers or 'Dragon King' events across diverse real-world scenarios.

Contribution

It develops new robust test statistics, reintroduces and improves inward sequential testing, and demonstrates their effectiveness in detecting meaningful outliers in heavy-tailed distributions.

Findings

MRS and SRS tests improve outlier detection robustness.

Inward testing is as powerful as outward testing and simpler to implement.

Application to real-world data reveals significant outliers linked to 'Dragon King' events.

Abstract

We introduce two ratio-based robust test statistics, max-robust-sum (MRS) and sum-robust-sum (SRS), designed to enhance the robustness of outlier detection in samples with exponential or Pareto tails. We also reintroduce the inward sequential testing method -- formerly relegated since the introduction of outward testing -- and show that MRS and SRS tests reduce susceptibility of the inward approach to masking, making the inward test as powerful as, and potentially less error-prone than, outward tests. Moreover, inward testing does not require the complicated type I error control of outward tests. A comprehensive comparison of the test statistics is done, considering performance of the proposed tests in both block and sequential tests, and contrasting their performance with classical test statistics across various data scenarios. In five case studies -- financial crashes, nuclear power generation accidents, stock market returns, epidemic fatalities, and city sizes -- significant outliers are detected and related to the concept of `Dragon King' events, defined as meaningful outliers that arise from a unique generating mechanism.