Semiparametric Estimates of the Long-Term Background Trend, Periodictiy, and Clustering Effect in Crime Data

• Activity Number: 182
• Type: Contributed
• Date/Time: Monday, August 1, 2016 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Jiancang Zhuang* and Jorge Mateau
• Companies: Institute of Statistical Mathematics and Universitat Jaume I de Castelló
• Keywords: spatiotemporal point process ; crime ; Hawkes process ; stochastic reconstruction ; peridicity ; clustering

Abstract

Past studies have shown that crime behaviors are clustered. This study proposes a spatio-temporal Hawkes-type point-process model, which includes a background component with daily and weekly periodicities and a clustering component that is triggered by previous events, for describing the occurrences of violence or robbery related to crimes in the city of Castellon, Spain, during 2012 and 2013. A nonparametric method, called stochastic reconstruction, is used to estimate each component, including daily and weekly periodicities of background rate, spatial background rate, long-term background trend, and the spatial and temporal response function in the triggering component, of the conditional intensity of the model. The results show that about 30 percent of the crimes can be explained by clustering.