Global Envelope Tests for Spatial Processes

• DOI: 10.1111/rssb.12172
• Publication Date: 2016-03-21T04:47:32Z
• Authors: Mari Myllymäki; Tomáš Mrkvička; Pavel Grabarnik; Henri Seijo; Ute Hahn
• Keywords: Envelope (radar)

Envelope tests are a popular tool in spatial statistics, where they used goodness-of-fit testing. These graphically compare an empirical function $T(r)$ with its simulated counterparts from the null model. However, type I error probability $\alpha$ is conventionally controlled for fixed distance $r$ only, whereas functions inspected on interval of distances $I$. In this study, we propose two approaches related to Barnard's Monte Carlo test building global envelope $I$:(1) ordering and based their $r$-wise ranks among each other, (2) construction envelopes deviation test. new allow priori selection yield $p$-values. We illustrate these using real point pattern data.