Theses and Dissertations

ORCID

https://orcid.org/0009-0007-8335-4603

Issuing Body

Mississippi State University

Advisor

Woody, Jonathan R.

Committee Member

Zhang, Jialin

Committee Member

Sepehrifar, Mohammad

Committee Member

Wu, Tung-Lung

Committee Member

Dang, Hai,

Date of Degree

12-13-2024

Original embargo terms

Visible MSU only 2 years

Document Type

Dissertation - Campus Access Only

Major

Mathematical Sciences

Degree Name

Doctor of Philosophy (Ph.D.)

College

College of Arts and Sciences

Department

Department of Mathematics and Statistics

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.

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