On Kernel-Based Intensity Estimation of Spatial Point Patterns on Linear Networks
将Diggle的非参数边缘校正核强度估计扩展到线性网络上的非齐次点模式，证明了无偏性并给出了方差表达式，通过芝加哥街头犯罪和西班牙卡斯特利翁反社会行为电话数据验证了方法。
We propose an extension of Diggle’s nonparametric edge-corrected kernel-based intensity estimator to the case of events coming from an inhomogenous point pattern on a linear network. We analyze its statistical properties, showing that it is an unbiased estimator of the first-order intensity; we also provide an expression for the variance, and comment on the appropriate bandwidth selection. Our estimator is compared with the current existing equal-split discontinuous kernel density estimator in terms of the mean integrated squared error (MISE). We then use our estimator on two real datasets. We first revisit street crimes in an area of Chicago, obtaining similar results to previously published ones based on a parametric intensity function. Then, we study network-based spatial events consisting of calls to the Police department reporting anti-social behavior in the city of Castellon (Spain).