Nonparametric Subset Scanning for Detection of Heteroscedasticity

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.

我们提出异方差子集扫描（Heteroscedastic Subset Scan, HSS）这一新颖方法，用于在回归场景中识别引发同方差性假设违背的协变量。将该问题视作异常模式检测任务，我们采用子集扫描技术，高效定位与异方差性最相关的协变量子集。通过模拟实验与真实数据集案例，我们证实HSS能够在多种场景下检测异方差性，涵盖现有全局检验效力不足的情形。此外，本方法的全局检验功效优于布罗斯尚-帕根检验（Breusch–Pagan test）等同类方法。本文的补充材料可在线获取。