Journal
JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
Volume 79, Issue 2, Pages 381-404Publisher
OXFORD UNIV PRESS
DOI: 10.1111/rssb.12172
Keywords
Deviation test; Functional depth; Global envelope test; Goodness-of-fit test; Monte Carlo p-value; Spatial point pattern
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Funding
- Academy of Finland [250860, 294162]
- Grant Agency of the Czech Republic [16-03708S]
- Russian Foundation for Basic Research grant [12-04-01527, 16-04-01348]
- Villum Foundation
- Academy of Finland (AKA) [294162, 250860, 294162, 250860] Funding Source: Academy of Finland (AKA)
- Villum Fonden [00008721] Funding Source: researchfish
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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 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: ordering the empirical and simulated functions on the basis of their r-wise ranks among each other, and the construction of envelopes for a deviation test. These new tests allow the a priori choice of the global and they yield p-values. We illustrate these tests by using simulated and real point pattern data.
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