Abstract

Testing whether two spatial point processes have the same spatial distribution is an important task that can be addressed from different perspectives. A Kolmogorov-Smirnov test with asymptotic calibration and a Cramer von Mises type test with bootstrap calibration have recently been developed to compare the first-order intensity of two observed patterns. Motivated by common practice in epidemiological studies, we introduce a regression test based on the relative risk function with two alternative bootstrap calibrations. This paper compares the performance of these nonparametric tests through both an intensive simulation study, and the application to wildfire and crime data. The three tests provide good calibrations of the null hypothesis for simulated Poisson and non-Poisson spatial point processes, but the Cramer von Mises and regression tests outperform the cost-efficient Kolmogorov-Smirnov test in terms of power. In the real data analysis we have seen that the Kolmogorov-Smirnov test does not detect differences between spatial point patterns when dealing with sparse data. In view of these results, it would be preferable using the Cramer von Mises or regression tests despite their higher computational demand.

摘要

测试两个空间点过程是否具有相同的空间分布是一项可以从不同角度解决的重要任务。最近开发了具有渐近校准的 Kolmogorov-Smirnov 检验和具有自举校准的 Cramer von Mises 型检验来比较两个观察到的模式的一阶强度。受流行病学研究中常见做法的启发，我们引入了一个基于相对风险函数的回归测试，该回归测试具有两个备选的自举校准。本文通过深入的模拟研究以及对野火和犯罪数据的应用，比较了这些非参数检验的性能。这三个测试为模拟的泊松和非泊松空间点过程提供了原假设的良好校准，但 Cramer von Mises 和回归测试在功效方面优于经济高效的 Kolmogorov-Smirnov 测试。在实际数据分析中我们看到，Kolmogorov-Smirnov 检验在处理稀疏数据时没有检测到空间点模式之间的差异。鉴于这些结果，最好使用 Cramer von Mises 或回归测试，尽管它们的计算需求更高。