Spatial Change Points Detection in Nonparametric Regression Models

Spatial heterogeneity is a defining feature of geospatial data and has attracted sustained attention. Spatial change points, defined as locations where the association patterns among variables undergoes a statistically significant structural shift, are a key manifestation of such heterogeneity. While change point detection methods are highly effective at identifying structural breaks in time series, their extension to spatial settings faces fundamental challenges, primarily because mainstream approaches inherently rely on the natural temporal ordering of observations, a feature that is absent in spatial data. To address this challenge, we propose two nonparametric change point detection methods requiring only observational data and geographic coordinates, where the kernel bandwidth both smooths the regression trend and defines the local scanning scale. The first constructs local discrepancy statistics based on kernel-smoothed residuals by comparing spatial association patterns across the four quadrants within circular neighborhoods defined by a kernel bandwidth. The second introduces a pseudo-temporal ordering by sorting coordinates within local strip-shaped windows and builds a cumulative sum process from the same residuals. Extensive simulations evaluate their performance across diverse spatial heterogeneity configurations, demonstrating strong detection power across scenarios. An application to air quality monitoring data from China validates their practical utility in real-world spatial analysis.