An Estimating Function Approach to Inference for Inhomogeneous Neyman–Scott Processes

Abstract

This article is concerned with inference for a certain class of inhomogeneous Neyman-Scott point processes depending on spatial covariates. Regression parameter estimates obtained from a simple estimating function are shown to be asymptotically normal when the "mother" intensity for the Neyman-Scott process tends to infinity. Clustering parameter estimates are obtained using minimum contrast estimation based on the K-function. The approach is motivated and illustrated by applications to point pattern data from a tropical rain forest plot.

Fast block variance estimation procedures for inhomogeneous spatial point processes

“…Similar results were obtained for the latter with other k * n values, and therefore we do not report them here. Our estimates are very similar to those of Guan & Loh (2007) and are slightly smaller than those of Waagepetersen (2007). On the basis of a 5% level of significance, we thus conclude that β 2 is significant but β 1 is not.…”

“…It holds for a broad class of inhomogeneous models including, but not limited to, the log-Gaussian Cox process (Møller et al, 1998), the inhomogeneous NeymanScott process (Waagepetersen, 2007) and any inhomogeneous process that is obtained by thinning a homogeneous process satisfying this condition. The following theorem, proved in Appendix 2, establishes the consistency ofV n .…”

“…Waagepetersen (2007) and Guan & Loh (2007) analyzed the same data and both used the first-order intensity function model λ(s) = exp{β 0 + β 1 E(s) + β 2 G(s)}, where E(s) and G(s) are the elevation and elevation gradient at s, respectively. By maximizing (1), Waagepetersen (2007) obtained the estimatesβ 1 = 0·02 andβ 2 = 5·84. To estimate the standard errors ofβ 1 andβ 2 , he used a plug-in method that assumes a parametric model for the pair correlation function.…”

“…Schoenberg (2005) showed thatβ is consistent for β for a wide class of spatial-temporal point process models, even if the process is not Poisson. Waagepetersen (2007) and Guan & Loh (2007) established asymptotic normality forβ for a class of inhomogeneous Neyman-Scott processes and a class of mixing point processes, respectively. To make inference about β, the variance ofβ needs to be estimated.…”

Spatial point process modeling applied to the assessment of risk factors associated with forest wildfires incidence in Castellón, Spain

“…The statistical analysis of the wildfire patterns for the years 2001-2006 in Castellón was done using the theory and methodology of spatial point processes (Cressie, 1993;Diggle, 2003, Møller andWaagepetersen, 2007). Although we could have followed the most common logistic and auto logistic approaches, those methods cannot be extended easily to different spatial scales.…”