## A Studentized Permutation Test for the Comparison of Spatial Point Patterns

Publikation: Working paperForskning

### Dokumenter

• Institut for Matematiske Fag
• Centre for Stochastic Geometry and Advanced Bioimaging
A new test is proposed for the hypothesis that two (or more) observed point patterns are realizations of the same spatial point process model. To this end, the point patterns are divided into disjoint quadrats, on each of which an estimate of Ripley's $K$-function is calculated. The two groups of empirical $K$-functions are compared by a permutation test using a studentized test statistic. The proposed test performs convincingly in terms of empirical level and power in a simulation study, even for point patterns where the $K$-function estimates on neighboring subsamples are not strictly exchangeable. It also shows improved behavior compared to a test suggested by Diggle et al. (1991, 2000) for the comparison of groups of independently replicated point patterns. In an application to two point patterns from pathology that represent capillary positions in sections of healthy and tumorous tissue, our studentized permutation test indicates statistical significance, although the patterns cannot be clearly distinguished by eye.
Originalsprog Engelsk Århus Institut for Matematiske Fag, Aarhus Universitet 23 Udgivet - dec. 2010

### Forskningsområder

• Nonparametric test, $K$-function, quadrat, spatial point processes, subsampling

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