Nonparametric Subset Scanning for Detection of Heteroscedasticity

Abstract

We propose heteroscedastic subset scan (HSS), a novel method for identifying covariates that are responsible for violations of the homoscedasticity assumption in regression settings. Viewing the problem as one of anomalous pattern detection, we use subset scanning techniques to efficiently identify the subset of covariates that are most “heteroscedastically relevant.” Through simulations and a real data example, we demonstrate that HSS is capable of detecting heteroscedasticity in a wide range of settings, including in cases where existing global tests lack power. Furthermore, the global power of our method compares favorably to methods such as the Breusch–Pagan test. Supplementary materials for this article are available online.

Keywords:

• Anomaly detection
• Model diagnostics
• Regression
• Scan statistics

Supplementary Materials

The online supplementary materials provide a basic R implementation of the HSS algorithm and the education expenditure data utilized in Section 5.5.

Acknowledgments

Evan Olawsky was originally an author on this paper. He has chosen to not participate in the revision, and to cede authorship of the paper.

Notes

1 We have found $\rho =1/2$ to be acceptable in practice.

Additional information

Funding

Charles R. Doss is partially funded by NSF grant DMS-1712664 and NSF grant DMS-1712706. Edward McFowland III gratefully acknowledges funding support from the NSF Program on Fairness in Artificial Intelligence in Collaboration with Amazon, grant IIS-2040898.