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A third‐order point process characteristic for multi‐type point processes

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  • Carlos Comas
  • Jorge Mateu
  • Aila Särkkä

Abstract

The description and analysis of spatial point patterns have mainly been based on first‐ and second‐order characteristics. However, and especially when analyzing complex and multivariate point patterns, the use of higher‐order characteristics would be more informative. In this paper, we introduce a third‐order characteristic for multi‐type point processes, which is based on the number of r‐close triples of points, where the three points are of three different types (species). This characteristic is useful, when the second‐order characteristics indicate that the three point patterns are pairwise uncorrelated but there is some relationship between triples of points. Furthermore, we conjecture that the new statistic can be used to test independence between the three point processes.

Suggested Citation

  • Carlos Comas & Jorge Mateu & Aila Särkkä, 2010. "A third‐order point process characteristic for multi‐type point processes," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 64(1), pages 19-44, February.
    • Handle: RePEc:bla:stanee:v:64:y:2010:i:1:p:19-44
    DOI: 10.1111/j.1467-9574.2009.00437.x
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    References listed on IDEAS

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    1. P. Grabarnik, 2002. "Goodness-of-fit test for complete spatial randomness against mixtures of regular and clustered spatial point processes," Biometrika, Biometrika Trust, vol. 89(2), pages 411-421, June.
    2. A. J. Baddeley & J. Møller & R. Waagepetersen, 2000. "Non‐ and semi‐parametric estimation of interaction in inhomogeneous point patterns," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 54(3), pages 329-350, November.
    3. K. Schladitz & A. J. Baddeley, 2000. "A Third Order Point Process Characteristic," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 27(4), pages 657-671, December.
    4. M. N. M. Van Lieshout & A. J. Baddeley, 1999. "Indices of Dependence Between Types in Multivariate Point Patterns," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 26(4), pages 511-532, December.
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