空间过程的全局包络检验
Global envelope tests for spatial processes
摘要：
包络检验是空间统计学中的一种常用工具，用于拟合优度检验。这些检验以图形方式比较经验函数$T(r)$与来自零模型的模拟对应函数。然而，传统上仅针对固定距离$r$来控制第一类错误概率$α$，而在距离间隔$I$上检查功能。在这项研究中，我们提出了两种方法相关的Barnard的蒙特卡罗测试建立全球包络测试$I$：（1）订购的经验和模拟功能的基础上，他们的$r$明智的排名，以及（2）的偏差测试的信封的建设。这些新的测试允许全局$α$的先验选择，并且它们产生$p$值。我们说明这些测试使用模拟和真实的点模式数据。
英文摘要：
Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical function $T(r)$ with its simulated counterparts from the null model. However, the type I error probability $α$ is conventionally controlled for a fixed distance $r$ only, whereas the functions are inspected on an interval of distances $I$. In this study, we propose two approaches related to Barnard's Monte Carlo test for building global envelope tests on $I$:(1) ordering the empirical and simulated functions based on their $r$-wise ranks among each other, and (2) the construction of envelopes for a deviation test. These new tests allow the a priori selection of the global $α$ and they yield $p$-values. We illustrate these tests using simulated and real point pattern data.
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