J-function for inhomogeneous spatio-temporal point processes
Journal article, 2015
We propose a new summary statistic for inhomogeneous intensity-reweighted moment stationarity spatio-temporal point processes. The statistic is defined in terms of the n-point correlation functions of the point process, and it generalizes the J-function when stationarity is assumed. We show that our statistic can be represented in terms of the generating functional and that it is related to the spatio-temporal K-function. We further discuss its explicit form under some specific model assumptions and derive ratio-unbiased estimators. We finally illustrate the use of our statistic in practice.
(reduced Palm measure) generating functional
K-function
J-function
inhomogeneous spatio-temporal point process
location-dependent thinning of hard core model
intensity-reweighted moment sta- tionarity
Papangelou conditional intensity
n-point correlation function
Poisson process
log- Gaussian Cox process
Author
Ottmar Cronie
Chalmers, Mathematical Sciences, Applied Mathematics and Statistics
Marie Colette N.M. Van Lieshout
Scandinavian Journal of Statistics
0303-6898 (ISSN) 1467-9469 (eISSN)
Vol. 2 562-579Subject Categories
Probability Theory and Statistics
Mathematical Analysis
DOI
10.1111/sjos.12123