We propose a new summary statistic for marked point patterns. The underlying principle is to compare the distance from a marked point to the nearest other marked point in the pattern to the same distance seen from an arbitrary point in space. Information about the range of interaction can be inferred, and the statistic is well-behaved under random mark allocation. We develop a range of Hanisch style kernel estimators to tackle the problems of exploding tail variance earlier associated with J-function plug-in estimators, and carry out an exploratory analysis of a forestry data set.

Geometric probability and stochastic geometry (msc 60D05), Point processes (msc 60G55), None of the above, but in MSC2010 section 62Gxx (msc 62G99), Spatial processes (msc 62M30)
CWI. Probability, Networks and Algorithms [PNA]
Signals and Images

van Lieshout, M.N.M. (2004). A J-function for marked point patterns. CWI. Probability, Networks and Algorithms [PNA]. CWI.