PASCAL - Pattern Analysis, Statistical Modelling and Computational Learning

A J-function for marked point patterns
Marie-Colette van Lieshout
Annals of the Institute of Statistical Mathematics Volume Annals of the Institute of Statistical Mathematics, Number 58, pp. 235-259, 2006.


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.

EPrint Type:Article
Project Keyword:Project Keyword UNSPECIFIED
Subjects:Learning/Statistics & Optimisation
Theory & Algorithms
ID Code:2395
Deposited By:Marie-Colette van Lieshout
Deposited On:22 November 2006