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Title: Analysis of circular interval-censored data motivated by aoristic data in criminology Authors:  Kees Mulder - Utrecht University (Netherlands) [presenting]
Stijn Ruiter - Netherlands Institute for the Study of Crime and Law Enforcement NSCR / Utrecht University (Netherlands)
Irene Klugkist - Utrecht University (Netherlands)
Abstract: Motivated by an application in criminology, methods are developed for parameteric and non-parametric density estimation on the circle when interval-censored data are given. In crime analysis, there is an interest to determine at what time of day crimes have happened, which leads to the analysis of circular data. The objective is to estimate the frequency of crime at any given time of the day, day of the week, or day of the year. However, victims of crimes such as theft and burglary often do not know when exactly the crime occurred, knowing only the time interval during which the crime must have happened. Therefore, the temporal information in crime data is often interval-censored. Current so-called aoristic analysis methods comprise mostly of histogram-like methods for density estimation. We extend these methods from a statistical perspective. It can be shown that standard aoristic analysis results in densities with a variance that is too high. We show how likelihood estimation can be adapted to work with interval-censored data. We fit parametric models based on the von Mises distribution and Bayesian semiparametric models based on the Dirichlet process. The advantage of these models is that they use all available information for the density estimation without the requirement to select an arbitrary bandwidth or something alike. These new methods are available as an R package.