Global envelope tests for spatial processes
TLDR
In this paper, two approaches related to Barnard's Monte Carlo test are proposed 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.Abstract:
Summary
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: 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 α and they yield p-values. We illustrate these tests by using simulated and real point pattern data.read more
Citations
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The accumulated persistence function, a new useful functional summary statistic for topological data analysis, with a view to brain artery trees and spatial point process applications.
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Directional Outlyingness for Multivariate Functional Data
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References
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