Some properties of local weighted second-order statistics for spatio-temporal point processes

Point process diagnostics based on weighted second-order statistics and their asymptotic properties

A new approach for point process diagnostics is presented. The method is based on extending second-order statistics for point processes by weighting each point by the inverse of the conditional intensity function at the point’s location. The result is generalized versions of the spectral density, R/S statistic, correlation integral and K-function, which can be used to test the fit of a complex ...

Spatial and Spatio-temporal Point Processes

The present paper gives the background to point processes in space and time. Some special types of spatial and spatio-temporal models of point processes are introduced with the emphasis to Cox processes. Their basic properties are described and some characteristics are calculated. The simulation of one of these models is shown. Introduction At present, the theory of point processes is well esta...

Boundary Crossing of Order Statistics Point Processes

This paper is concerned with the first crossing of an order statistic point process through general moving boundaries. Our purpose is to determine exact boundary crossing probabilities in both one and two boundary cases. Simple recursive methods are obtained that exploit an underlying algebraic structure of polynomial type. This structure is a direct consequence of the order statistic property....

A Partial Likelihood for Spatio-temporal Point Processes

A J-function for Inhomogeneous Spatio-temporal Point Processes

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 th...