Globally intensity-reweighted estimators for $K$- and pair correlation functions

Abstract: We introduce new estimators of the inhomogeneous $K$-function and the pair correlation function of a spatial point process as well as the cross $K$-function and the cross pair correlation function of a bivariate spatial point process under the assumption of second-order intensity-reweighted stationarity. These estimators rely on a 'global' normalization factor which depends on an aggregation of the intensity function, whilst the existing estimators depend 'locally' on the intensity function at the individual observed points. The advantages of our new global estimators over the existing local estimators are demonstrated by theoretical considerations and a simulation study.