Estimating functions for inhomogeneous spatial point processes with incomplete covariate data

Abstract

The R package spatstat provides a very flexible and useful framework for analysing spatial point patterns. A fundamental feature is a procedure for fitting spatial point process models depending on covariates. However, in practice one often faces incomplete observation of the covariates and this leads to parameter estimation error which is difficult to quantify. In this paper, we introduce a Monte Carlo version of the estimating function used in spatstat for fitting inhomogeneous Poisson processes and certain inhomogeneous cluster processes. For this modified estimating function, it is feasible to obtain the asymptotic distribution of the parameter estimators in the case of incomplete covariate information. This allows a study of the loss of efficiency due to the missing covariate data.