Application of the double kernel density approach to the multivariate analysis of attributeless event point datasets

Attributeless event point datasets (AEPDs) are datasets composed of discrete events or observations defined by their geographical location only and lacking any other additional attributes. Examples of such datasets include spotted criminal events, road accidents and residential locations of disease patients. A commonly used approach to the analysis of such datasets involves their aggregation into predefined areal units, such as neighborhoods or census tracts. However, this approach does not perform effectively when the events of interests are geographically localized and the number of areal units available for aggregation is small. An alternative approach to the analysis of AEPDs is based on double kernel density (DKD) smoothing, according to which events of interest are transformed into continuous density surfaces and then normalized by the density of the entire population from which the events of interest are drawn. In the present study, the applicability of the DKD approach to multivariate analysis is tested for estimation consistency, sensitivity to the number of input observations and potential bias attributed to the spatial dependency of neighboring observations. Our analysis indicates that the DKD approach provides reasonably stable and consistent estimates, if the following three preconditions are met: (a) the kernel estimation parameters are properly defined, (b) the number of reference points, used for transformation of continuous DKD surfaces into discrete observations, is sufficiently large, and (c) the spatial dependency of neighboring observations is taken into account using spatial analysis tools.