Testing uniformity of a spatial point pattern

Lai Ping Ho; Sung Nok Chiu

doi:10.1198/106186007X208966

Testing uniformity of a spatial point pattern

Lai Ping Ho^*, Sung Nok Chiu

^*Corresponding author for this work

Department of Mathematics

Research output: Contribution to journal › Journal article › peer-review

7 Citations (Scopus)

12 Downloads (Pure)

Abstract

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.

Original language	English
Pages (from-to)	378-398
Number of pages	21
Journal	Journal of Computational and Graphical Statistics
Volume	16
Issue number	2
DOIs	https://doi.org/10.1198/106186007X208966
Publication status	Published - Jun 2007

Scopus Subject Areas

Statistics and Probability
Discrete Mathematics and Combinatorics
Statistics, Probability and Uncertainty

User-Defined Keywords

Complete spatial randomness
Discrepancy
Quasi-Monte Carlo method
Spatial point process

Access to Document

10.1198/106186007X208966

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title = "Testing uniformity of a spatial point pattern",

abstract = "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.",

keywords = "Complete spatial randomness, Discrepancy, Quasi-Monte Carlo method, Spatial point process",

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note = "Funding Information: We thank an associate editor and the referees for helpful comments. 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.",

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AU - Chiu, Sung Nok

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N2 - 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.

AB - 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.

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Testing uniformity of a spatial point pattern

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