A spatial randomness test based on the box-counting dimension

Yolanda Caballero (), Ramón Giraldo () and Jorge Mateu ()
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Yolanda Caballero: Universidad Nacional de Colombia
Ramón Giraldo: Universidad Nacional de Colombia
Jorge Mateu: Universidad Jaume I

AStA Advances in Statistical Analysis, 2022, vol. 106, issue 3, No 11, 499-524

Abstract: 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.

Keywords: Box-counting dimension; Complete spatial randomness Fractal dimension; Poisson distribution; Spatial point patterns (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1007/s10182-021-00434-4

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