Local inhomogeneous weighted summary statistics for marked point processes

Summary statistics for inhomogeneous marked point processes

We propose new summary statistics for intensity-reweighted moment stationary marked point processes with particular emphasis on discrete marks. The new statistics are based on the n-point correlation functions and reduce to cross J and D-functions when stationarity holds. We explore the relationships between the various functions and discuss their explicit forms under specific model assumptions...

Local Block Bootstrap for Inhomogeneous Poisson Marked Point Processes

The asymptotic theory for the sample mean of a marked point process in d dimensions is established, allowing for the possibility that the underlying Poisson point process is inhomogeneous. A novel local block bootstrap method for resampling inhomogeneous Poisson marked point processes is introduced, and its consistency is proven for the sample mean and related statistics. Finite-sample simulati...

Technical supplement to : “ Local Block Bootstrap for Inhomogeneous Poisson Marked Point Processes ”

Moment estimation for statistics from marked point processes

In spatial statistics the data typically consist of measurements of some quantity at irregularly scattered locations; in other words, the data form a realization of a marked point process. In this paper, we formulate subsampling estimators of the moments of general statistics computed from marked point process data, and establish their L2 consistency. The variance estimator in particular can be...

Variance Estimation for Statistics Computed from Inhomogeneous Spatial Point Processes

This paper introduces a new approach to estimate the variance of statistics that are computed from an inhomogeneous spatial point process. The proposed approach is based on the assumption that the observed point process can be thinned to be a second-order stationary point process, where the thinning probability depends only on the first-order intensity function of the (unthinned) original proce...