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arXiv · 1307.0239

Global envelope tests for spatial processes

Mari Myllymäki·Tomás Mrkvicka·Pavel Grabarnik·Henri Seijo·Ute Hahn
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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 function $T(r)$ with its simulated counterparts from the null model. However, the type I error probability $\alpha$ 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 $\alpha$ and they yield $p$-values. We illustrate these tests using simulated and real point pattern data.

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Mari Myllymäki, Tomás Mrkvicka, Pavel Grabarnik, Henri Seijo, Ute Hahn. 2013-06-30. Global envelope tests for spatial processes. https://doi.org/10.1111/rssb.12172

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