Department of Mathematics
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.
Discrepancy, Longleaf pine data, Spatial point process, Stationarity test
Source Publication Title
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.
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.
Link to Publisher's Edition
Chiu, S., & Liu, K. (2013). Stationarity tests for spatial point processes using discrepancies. Biometrics, 69 (2), 497-507. https://doi.org/10.1111/biom.12031