Nonparametric Method for Modeling Clustering Phenomena in Emergency Calls Under Spatial-Temporal Self-Exciting Point Processes

In this paper, a nonparametric spatial-temporal self-exciting point process is proposed to model clustering features in emergency calls. Gaussian kernel density functions are considered. The expectation-maximization algorithm is adopted for estimating the model. A simulation study is designed to carefully examine the performance of the proposed nonparametric method. The spatial-temporal patterns of the emergency calls in Montgomery County of Pennsylvania are studied using the proposed nonparametric model. The results demonstrate that the proposed nonparametric model captures the clustering phenomena present in the emergency calls from Montgomery County very well. Further, the proposed parameter estimation method results in robust and precise estimates.