Global envelope tests for spatial processes
Mari Myllymäki, Tomáš Mrkvička, Pavel Grabarnik, Henri Seijo, Ute Hahn
Journal of the Royal Statistical Society: Series B (Statistical Methodology) · 2017 · Volume 79 · Issue 2
Abstract
Envelope tests are a popular tool in spatial statistics, where they are used in goodness-of-fit testing. These tests graphically compare an empirical functionT(r) with its simulated counterparts from the null model. However, the type I error probabilityαis conventionally controlled for a fixed distanceronly, whereas the functions are inspected on an interval of distancesI. In this study, we propose two approaches related to Barnard's Monte Carlo test for building global envelope tests onI: ordering the empirical and simulated functions on the basis of theirr-wise ranks among each other, and the construction of envelopes for a deviation test. These new tests allow thea priorichoice of the globalαand they yieldp-values. We illustrate these tests by using simulated and real point pattern data.
Keywords
Deviation test, Functional depth, Global envelope test, Goodness-of-fit test, Monte Carlop-value, Spatial point pattern
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