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A spatial randomness test based on the box-counting dimension

Author

Listed:
  • Yolanda Caballero

    (Universidad Nacional de Colombia)

  • Ramón Giraldo

    (Universidad Nacional de Colombia)

  • Jorge Mateu

    (Universidad Jaume I)

Abstract

Statistical modelling of a spatial point pattern often begins by testing the hypothesis of spatial randomness. Classical tests are based on quadrat counts and distance-based methods. Alternatively, we propose a new statistical test of spatial randomness based on the fractal dimension, calculated through the box-counting method providing an inferential perspective contrary to the more often descriptive use of this method. We also develop a graphical test based on the log–log plot to calculate the box-counting dimension. We evaluate the performance of our methodology by conducting a simulation study and analysing a COVID-19 dataset. The results reinforce the good performance of the method that arises as an alternative to the more classical distances-based strategies.

Suggested Citation

  • Yolanda Caballero & Ramón Giraldo & Jorge Mateu, 2022. "A spatial randomness test based on the box-counting dimension," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 106(3), pages 499-524, September.
    • Handle: RePEc:spr:alstar:v:106:y:2022:i:3:d:10.1007_s10182-021-00434-4
    DOI: 10.1007/s10182-021-00434-4
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    References listed on IDEAS

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    2. Breslin, M.C. & Belward, J.A., 1999. "Fractal dimensions for rainfall time series," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 48(4), pages 437-446.
    3. Baddeley, Adrian & Turner, Rolf & Mateu, Jorge & Bevan, Andrew, 2013. "Hybrids of Gibbs Point Process Models and Their Implementation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 55(i11).
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