Testing spatial symmetry using contingency tables based on nearest neighbor relations
type: Item
instance of: scholarly article
title: Testing spatial symmetry using contingency tables based on nearest neighbor relations
zbMATH Open document ID: 1328.62360
DOI: 10.1155/2014/698296
author: Elvan Ceyhan
published in: The Scientific World Journal. Probability and Statistics
publication date: 2016-01-13T00:00:00Z
review text: Summary: We consider two types of spatial symmetry, namely, symmetry in the mixed or shared nearest neighbor (NN) structures. We use Pielou's and Dixon's symmetry tests which are defined using contingency tables based on the NN relationships between the data points. We generalize these tests to multiple classes and demonstrate that both the asymptotic and exact versions of Pielou's first type of symmetry test are extremely conservative in rejecting symmetry in the mixed NN structure and hence should be avoided or only the Monte Carlo randomized version should be used. Under RL, we derive the asymptotic distribution for Dixon's symmetry test and also observe that the usual independence test seems to be appropriate for Pielou's second type of test. Moreover, we apply variants of Fisher's exact test on the shared NN contingency table for Pielou's second test and determine the most appropriate version for our setting. We also consider pairwise and one-versus-rest type tests in post hoc analysis after a significant overall symmetry test. We investigate the asymptotic properties of the tests, prove their consistency under appropriate null hypotheses, and investigate finite sample performance of them by extensive Monte Carlo simulations. The methods are illustrated on a real-life ecological data set.
Mathematics Subject Classification ID: 62H17
Mathematics Subject Classification ID: 62F03
zbMATH DE Number: 6529683
Wikidata QID: Q51104295
describes a project that uses: spatstat
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/698296
OpenAlex ID: W2033521968
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description: scientific article; zbMATH DE number 6529683