Caballero Yolanda, Giraldo Ramón, Mateu Jorge
Department of Statistics, Universidad Nacional de Colombia, Bogotá, Colombia.
Department of Mathematics, Universidad Jaume I, Castellón, Spain.
Adv Stat Anal. 2022;106(3):499-524. doi: 10.1007/s10182-021-00434-4. Epub 2022 Jan 5.
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.
空间点模式的统计建模通常始于检验空间随机性的假设。经典检验基于方格计数和基于距离的方法。另外，我们提出了一种基于分形维数的空间随机性新统计检验方法，该分形维数通过盒计数法计算得出，提供了一种与该方法更常见的描述性用途相反的推断视角。我们还开发了一种基于对数-对数图的图形检验方法来计算盒计数维数。我们通过进行模拟研究和分析一个新冠病毒疾病（COVID-19）数据集来评估我们方法的性能。结果强化了该方法作为更经典的基于距离策略的替代方法所具有的良好性能。
