Statistics PhD Defense - 10/16/24

Abstract: This dissertation examines a method for detecting clusters in financial loan amount data. After a literature review of scan statistics, order statistics, and extreme value theory, this study introduces a method that uses a scan statistic approach for anomaly detection, along with a tuning parameter that can help with any model uncertainty that may appear. Once these methods are applied on the lower tail on the financial data and clusters are detected, the methods are then extended and modified to get a better handle on the upper tail of the data. The upper tail is first fit by using a peaks-over-threshold approach. The data in the upper tail is then transformed to the generalized Pareto CDF transform, and the scan-based method is applied to the transformed data to identify anomalous loan amounts in the upper tail. These methods were put to a case study and used on two different banks that participated in the Paycheck Protection Program, a program that was previously linked with misreporting and fraud.