Bandwidth selection for kernel intensity estimators for spatial point processes

Bethany J. Macdonald, Tilman M. Davies and Martin L. Hazelton

Scandinavian Journal of Statistics, 2025, vol. 52, issue 3, 1111-1137

Abstract: Intensity estimation through kernel smoothing is a popular non‐parametric method of describing the characteristics of an underlying spatial point process. Key to the accuracy of this estimate is the choice of bandwidth. Too large or small a bandwidth can lead to features in the intensity being lost or to the introduction of artefacts. There are many available methods of bandwidth selection for spatial point patterns, but no consensus on the best option. Popular methods and software default options lead to very different intensity estimates and contrasting conclusions about the data that can be difficult to reconcile. In response, we propose new bandwidth selectors with more stable and consistent performance. These are adapted from popular plug‐in and cross‐validation techniques developed for general multivariate density estimation. The theoretical and practical performance of these proposed methods is explored and compared with other available methods in both simulated and real‐data scenarios. We find that our proposed methods perform consistently well across a range of different intensity patterns. We end with a discussion on the implications of edge effects when applying these methods, given the constrained windows in which spatial point patterns are often observed.

Date: 2025
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