Document Type

Journal Article

Department/Unit

Department of Mathematics

Language

English

Abstract

For testing stationarity of a given spatial point pattern, Guan (2008) proposed a model-free statistic, based on the deviations between observed and expected counts of points in expanding regions within the sampling window. This article extends his method to a general class of statistics by incorporating also such information when points are projected to the axes and by allowing different ways to construct regions in which the deviations are considered. The limiting distributions of the new statistics can be expressed in terms of integrals of a Brownian sheet and hence asymptotic critical values can be approximated. A simulation study shows that the new tests are always more powerful than that of Guan. When applied to the longleaf pine data where Guan's test gave an inconclusive answer, the new tests indicate a clear rejection of the stationarity hypothesis. © 2013, The International Biometric Society.

Keywords

Discrepancy, Longleaf pine data, Spatial point process, Stationarity test

Publication Date

2013

Source Publication Title

Biometrics

Volume

69

Issue

2

Start Page

497

End Page

507

Publisher

Wiley

Peer Reviewed

1

Copyright

This is the peer reviewed version of the following article: Chiu, S. N. and Liu, K. I. (2013), Stationarity Tests for Spatial Point Processes using Discrepancies. Biom, 69: 497–507. doi:10.1111/biom.12031, which has been published in final form at https://dx.doi.org/ 10.1111/biom.12031. This article may be used for non-commercial purposes in accordance with Wiley Terms and Conditions for Self-Archiving.

Funder

Research supported by a GRF grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (project no. HKBU200710) and Faculty Research Grants (FRG2/08-09/094 and FRG2/09-10/062) of Hong Kong Baptist University.

DOI

10.1111/biom.12031

Link to Publisher's Edition

http://dx.doi.org/10.1111/biom.12031

ISSN (print)

0006341X

ISSN (electronic)

15410420

Included in

Mathematics Commons

Share

COinS