 2013 Royal Statistical Society 0035–9254/14/63123 Appl. Statist. (2014) 63, Part 1, pp. 123–140 Characterizing spatial and chronological target selection of serial offenders Amanda S. Hering Colorado School of Mines, Boulder, USA and Sean Bair Bair Analytics, Highlands Ranch, USA [Received December 2011. Final revision April 2013] Summary. Using 31 unique crime series from two US cities, the spatial pattern that individual criminal decision makers follow is investigated. Locations within a city vary in the likelihood for crimes of a given type to occur, and this is accounted for by using kernel density estimation based on all crimes of each type. Kernel density estimation is highly influenced by the bandwidth, so an objective approach is used to select the estimate. Then, the kernel density estimate for each type of crime is incorporated in an inhomogeneous K -function that can identify significant spatial clustering and/or uniformity at various spatial scales for each crime series. We find that robbery series are more likely to exhibit uniformity than burglary series, which tend to show strong clustering. In addition, the order in which new crimes are added to a series is found to follow an interesting pattern that does not always support the theory of offender as forager in which criminals first cluster crimes and then gradually disperse them. Half of the robbery series exhibit a spatial distribution that begins dispersed and develops clusters as increasingly more events are added to the series, indicating that they often return to locations of earlier crimes after having committed crimes elsewhere. Keywords: Clustering; Crime series; Kernel density estimation; K -function; Monte Carlo tests; Point patterns 1. Introduction The spatial distribution of all crimes, usually of a particular type, has been widely researched. These types of analyses use crime data that have been aggregated to census units or police jurisdictions and are useful for police resource allocation and planning (e.g. Mohler et al. (2011), Tita and Radil (2010), Bernasco (2010), Berestycki and Nadal (2010), Chainey et al. (2008), Grubesic and Mack (2008), McLafferty et al. (2000) and Ratcliffe and McCullagh (1999)). Their conclusions are also informative for characterizing, for example, how burglars in a given region generally behave, but they do not address how one individual burglar chooses targets spatially. However, a minority of citizens are responsible for the majority of crimes (Paulsen et al., 2009; Innes et al., 2005; Wolfgang et al., 1972) and, by studying repeat offenders, law enforcement agencies may begin to understand the systematic behaviour of these individuals. Studying crime series, two or more similar crimes committed by the same decision maker (Paulsen et al., 2009), is inherently difficult owing to a lack of quality data. Ideally, serial offenders are apprehended before their series grow very long; thus, patience is required to collect Address for correspondence: Amanda S. Hering, Department of Applied Mathematics and Statistics, Colorado School of Mines, Golden, CO 80401, USA. E-mail: ahering@mines.edu