Department of Mathematics
For a spatial point pattern observed in a bounded window, we propose using discrepancies, which are measures of uniformity in the quasi-Monte Carlo method, to test the complete spatial randomness hypothesis. Tests using these discrepancies are in fact goodness-of-fit tests for uniform distribution. The discrepancies are free from edge effects and, unlike the popular maximum absolute pointwise difference statistic of a summary function over a suitably chosen range, do not have an arbitrary parameter. Simulation studies show that they are often more powerful when a given pattern is a realization of a process with long-range interaction or a nonstationary process. © 2007 American Statistical Association.
Complete spatial randomness, Discrepancy, Quasi-Monte Carlo method, Spatial point process
Source Publication Title
Journal of Computational and Graphical Statistics
Taylor & Francis
This is an Accepted Manuscript of an article published by Taylor & Francis in Journal of Computational and Graphical Statistics on 5-31-2007, available online: http://www.tandfonline.com/10.1198/106186007X208966.
This research was supported by grants from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project Numbers HKBU2048/02P and HKBU200503) and an FRG grant from the Hong Kong Baptist University.
Link to Publisher's Edition
Ho, Lai Ping, and Sung Nok Chiu. "Testing uniformity of a spatial point pattern." Journal of Computational and Graphical Statistics 16.2 (2007): 378-398.