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

TL;DR

This paper proposes new globally normalized estimators for inhomogeneous spatial point process functions, offering advantages over traditional local estimators through theoretical analysis and simulations.

Contribution

It introduces globally intensity-reweighted estimators for $K$- and pair correlation functions, improving upon existing local estimators under second-order intensity-reweighted stationarity.

Findings

Global estimators outperform local ones in simulations.

Theoretical advantages include reduced bias and variance.

Applicable to bivariate spatial point processes.

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.