Inference for low‐ and high‐dimensional inhomogeneous Gibbs point processes

Abstract

Gibbs point processes (GPPs) constitute a large and flexible class of spatial point processes with explicit dependence between the points. They can model attractive as well as repulsive point patterns. Feature selection procedures are an important topic in high‐dimensional statistical modeling. In this paper, a composite likelihood (in particular pseudo‐likelihood) approach regularized with convex and nonconvex penalty functions is proposed to handle statistical inference for possibly high‐dimensional inhomogeneous GPPs. We particularly investigate the setting where the number of covariates diverges as the domain of observation increases. Under some conditions provided on the spatial GPP and on penalty functions, we show that the oracle property, consistency and asymptotic normality hold. Our results also cover the low‐dimensional case which fills a large gap in the literature. Through simulation experiments, we validate our theoretical results and finally, an application to a tropical forestry dataset illustrates the use of the proposed approach.