Estimating second-order characteristics of inhomogeneous spatio-temporal point processes: influence of edge correction methods and intensity estimates

Abstract: We restrict our attention to space-time point pattern data for which we have a single realisation within a finite region. Second-order characteristics are used to analyse the spatio-temporal structure of the underlying point process. In particular, the space-time inhomogeneous pair correlation function and $K$-function measure the spatio-temporal clustering/regularity and the spatio-temporal interaction, and thus help with model choice. Non-parametric estimators of the second-order characteristics require information from outside the study region, resulting to the so-called edge effects which have to be corrected, and depend on first-order characteristics, which have to be estimated in practice. Here, we extend classical edge correction factors to the spatio-temporal setting and compare the performance of the related estimators for stationary/non-stationary and/or isotropic/anisotropic point patterns. Then, we explore the influence of estimated intensity function on these estimators.