Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

We develop a model-free isotropy test for spatial point patterns. The proposed test statistic assesses the discrepancy between the uniform distribution and the empirical normalised reduced second-order moment measure of a sector of increasing central angle. The null distribution of the test statistic is approximated by the empirical distribution obtained from bootstrap-type samples, which are generated by a stochastic procedure reconstructing independent isotropic patterns that resemble the spatial structure of the given point pattern, without specifying any underlying model. Simulation studies show that, when compared with the asymptotic χ2-test by Guan et al. (2006), the powers of the proposed test are more robust to different choices of user-chosen parameter. When applied to patterns of amacrine cells and Spanish towns, the bootstrap-type test clearly suggests rejection for the former and not rejection for the latter, while the asymptotic χ2-test is not conclusive in either case.

Keywords

Anisotropy, Bootstrap, Model-free, Orientation analysis, Reduced second-order moment measure

Publication Date

1-2-2016

Source Publication Title

Spatial Statistics

Issue

15

Start Page

56

End Page

69

Publisher

Elsevier

Peer Reviewed

1

Copyright

Copyright © 2015 Elsevier Ltd. All rights reserved.

Funder

This research was supported by GRF grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Nos. 200710 and 12301215).

DOI

10.1016/j.spasta.2015.12.002

ISSN (print)

22116753

Available for download on Thursday, March 01, 2018

Included in

Mathematics Commons

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