Statistical analysis of point processes often assumes that the underlying process is isotropic in the sense that its distribution is invariant under rotation. For point processes on ${ℝ}^2$, some tests based on the K‐function and nearest neighbour orientation function have been proposed to check such an assumption. However, anisotropy and directional analysis need proper caution when dealing with point processes on linear networks, as the implicit geometry of the network forces particular directions that the points of the pattern have to necessarily meet. In this paper, we adapt such tests to the case of linear networks and discuss how to use them to detect particular directional preferences, even at some angles that are different from the main angles imposed by the network. Through a simulation study, we check the performance of our proposals under different settings, over a linear network and a dendrite tree, showing that they are able to precisely detect the directional preferences of the points in the pattern, regardless the type of spatial interaction and the geometry of the network. We use our tests to highlight the directional preferences in the spatial distribution of traffic accidents in Barcelona (Spain), during 2019, and in Medellin (Colombia), during 2016.

中文翻译：

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线性网络上点模式的方向分析

对点过程的统计分析通常假设基础过程是各向同性的，因为它的分布在旋转下是不变的。对于点处理${ℝ}^{\mathrm{2个}}$，一些基于K的测试提出了函数和最近邻取向函数来检验这种假设。但是，在处理线性网络上的点过程时，各向异性和方向分析需要适当注意，因为网络的隐式几何结构会迫使图案的点必须满足的特定方向。在本文中，我们将此类测试调整为适合线性网络的情况，并讨论如何使用它们来检测特定的方向性偏好，即使在某些角度与网络施加的主角度不同的情况下也是如此。通过仿真研究，我们通过线性网络和树状树检查了不同设置下建议的性能，表明它们能够准确检测出模式中各点的方向性偏好，无论空间互动的类型和网络的几何形状如何。我们使用我们的测试来突出显示2019年巴塞罗那（西班牙）和2016年麦德林（哥伦比亚）交通事故在空间分布上的方向性偏好。