Abstract:Public procurement is vulnerable to error, fraud and corruption, yet high transaction volumes overwhelm oversight. While research often focuses on tender-stage anomalies, post-award payments remain underexplored. Since labelled datasets are rare and existing methods such as Benford's Law face restrictive assumptions, there is a need for additional interpretable, unsupervised frameworks that augment oversight and simplify management. This paper introduces the Structural Heterogeneity Index (SHI), a composite statistic for one-dimensional samples defined by four components: modality, asymmetry, tail behaviour, and structural dispersion. The Payment Heterogeneity Index (PHI) is its multiplicative instance for post-award payments. PHI combines a tail-behaviour component, sensitive to outliers and point clustering, with a structural-dispersion component summarising payment regime architecture. Structural dispersion is computed via Gaussian Mixture Model (GMM) estimation, integrating within-regime variability, prevalence, and separation from the dominant mode. Applied to UK municipal procurement data, PHI isolates a financially significant cohort (10.1% of high-volume suppliers) whose structural signatures deviate from the population and interact with recurring payment anchors. Permutation and Kolmogorov-Smirnov tests confirm that high-PHI suppliers exhibit statistically significant structural differences. A forensic review by a Certified Fraud Examiner supports the plausibility of the prioritised cases. Comparison shows PHI uniquely identifies regime separation obscured by metrics like the Coefficient of Variation (\r{ho}=0.310). PHI functions as an effective discovery tool where no confirmed labels exist, offering a transparent, lightweight screening mechanism for post-award oversight.
| Subjects: | Econometrics (econ.EM); Machine Learning (cs.LG); Statistical Finance (q-fin.ST); Applications (stat.AP) |
| Cite as: | arXiv:2605.12547 [econ.EM] |
| (or arXiv:2605.12547v1 [econ.EM] for this version) | |
| https://doi.org/10.48550/arXiv.2605.12547 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Kyriakos Christodoulides Dr [view email]
[v1]
Sat, 9 May 2026 20:59:29 UTC (1,321 KB)