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A Studentized Permutation Test for the Comparison of Spatial Point Patterns

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  • Ute Hahn

Abstract

In this study, a new test is proposed for the hypothesis that two (or more) observed point patterns are realizations of the same spatial point process model. To this end, the point patterns are divided into disjoint quadrats, on each of which an estimate of Ripley’s K -function is calculated. The two groups of empirical K -functions are compared by a permutation test using a Studentized test statistic. The proposed test performs convincingly in terms of empirical level and power in a simulation study, even for point patterns where the K -function estimates on neighboring subsamples are not strictly exchangeable. It also shows improved behavior compared with a test suggested by Diggle et al. for the comparison of groups of independently replicated point patterns. In an application to two point patterns from pathology that represent capillary positions in sections of healthy and cancerous tissue, our Studentized permutation test indicates statistical significance, although the patterns cannot be clearly distinguished by the eye.

Suggested Citation

  • Ute Hahn, 2012. "A Studentized Permutation Test for the Comparison of Spatial Point Patterns," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 107(498), pages 754-764, June.
    • Handle: RePEc:taf:jnlasa:v:107:y:2012:i:498:p:754-764
    DOI: 10.1080/01621459.2012.688463
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    Cited by:

    1. Stefano Bonnini & Getnet Melak Assegie & Kamila Trzcinska, 2024. "Review about the Permutation Approach in Hypothesis Testing," Mathematics, MDPI, vol. 12(17), pages 1-29, August.
    2. Tomáš Mrkvička & Tomáš Roskovec & Michael Rost, 2021. "A Nonparametric Graphical Tests of Significance in Functional GLM," Methodology and Computing in Applied Probability, Springer, vol. 23(2), pages 593-612, June.
    3. Jonatan A. González & Bernardo M. Lagos-Álvarez & Jorge Mateu, 2021. "Two-way layout factorial experiments of spatial point pattern responses in mineral flotation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 1046-1075, December.
    4. Baddeley, Adrian & Hardegen, Andrew & Lawrence, Thomas & Milne, Robin K. & Nair, Gopalan & Rakshit, Suman, 2017. "On two-stage Monte Carlo tests of composite hypotheses," Computational Statistics & Data Analysis, Elsevier, vol. 114(C), pages 75-87.
    5. Laura Anton-Sanchez & Pedro Larrañaga & Ruth Benavides-Piccione & Isabel Fernaud-Espinosa & Javier DeFelipe & Concha Bielza, 2017. "Three-dimensional spatial modeling of spines along dendritic networks in human cortical pyramidal neurons," PLOS ONE, Public Library of Science, vol. 12(6), pages 1-14, June.
    6. Łukasz Smaga & Jin‐Ting Zhang, 2020. "Linear hypothesis testing for weighted functional data with applications," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(2), pages 493-515, June.
    7. Ute Hahn & Eva B. Vedel Jensen, 2016. "Hidden Second-order Stationary Spatial Point Processes," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(2), pages 455-475, June.

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