  In the analysis of spatial point patterns on linear networks, a critical
statistical objective is estimating the first-order intensity function,
representing the expected number of points within specific subsets of the
network. Typically, non-parametric approaches employing heating kernels are
used for this estimation. However, a significant challenge arises in selecting
appropriate bandwidths before conducting the estimation. We study an intensity
estimation mechanism that overcomes this limitation using adaptive estimators,
where bandwidths adapt to the data points in the pattern. While adaptive
estimators have been explored in other contexts, their application in linear
networks remains underexplored. We investigate the adaptive intensity estimator
within the linear network context and extend a partitioning technique based on
bandwidth quantiles to expedite the estimation process significantly. Through
simulations, we demonstrate the efficacy of this technique, showing that the
partition estimator closely approximates the direct estimator while drastically
reducing computation time. As a practical application, we employ our method to
estimate the intensity of traffic accidents in a neighbourhood in Medellin,
Colombia, showcasing its real-world relevance and efficiency.

Methodology;Applications