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A J ‐function for Inhomogeneous Spatio‐temporal Point Processes
Author(s) -
Cronie O.,
Van Lieshout M. N. M.
Publication year - 2015
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/sjos.12123
Subject(s) - mathematics , point process , statistic , estimator , moment (physics) , score , function (biology) , point (geometry) , sufficient statistic , statistics , physics , geometry , classical mechanics , evolutionary biology , biology
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. © 2014 Board of the Foundation of the Scandinavian Journal of Statistics