We propose a computationally efficient and statistically principled method for kernel smoothing of point pattern data on a linear network. The point locations, and the network itself, are convolved with a two‐dimensional kernel and then combined into an intensity function on the network. This can be computed rapidly using the fast Fourier transform, even on large networks and for large bandwidths, and is robust against errors in network geometry. The estimator is consistent, and its statistical efficiency is only slightly suboptimal. We discuss bias, variance, asymptotics, bandwidth selection, variance estimation, relative risk estimation and adaptive smoothing. The methods are used to analyse spatially varying frequency of traffic accidents in Western Australia and the relative risk of different types of traffic accidents in Medellín, Colombia.

中文翻译：

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使用二维卷积的大型网络上点模式的快速内核平滑

我们提出了一种用于线性网络上的点模式数据的内核平滑的计算有效且统计原理的方法。将点位置以及网络本身与二维内核进行卷积，然后组合为网络上的强度函数。即使在大型网络和大带宽上，也可以使用快速傅里叶变换快速计算出该值，并且对于网络几何结构中的错误具有鲁棒性。估计量是一致的，其统计效率仅略次优。我们讨论偏差，方差，渐近，带宽选择，方差估计，相对风险估计和自适应平滑。该方法用于分析西澳大利亚州交通事故的空间变化频率以及哥伦比亚麦德林不同类型交通事故的相对风险。