On minimum contrast method for multivariate spatial point processes

Abstract

The minimum contrast (MC) method, as compared to the likelihood-based methods, is a computationally efficient method for estimation and inference of parametric stationary spatial point processes. This advantage becomes more pronounced when working with complex point process models, such as multivariate log-Gaussian Cox processes (LGCP). Despite its practical importance, there is very little work on the MC method for multivariate point processes. The aim of this article is to introduce a new MC method for parametric multivariate stationary spatial point processes. A contrast function is calculated based on the trace of the power of the difference between the conjectured K-function matrix and its nonparametric unbiased edge-corrected estimator. Under regular assumptions, the asymptotic normality of the MC estimator of the model parameters is derived. The performance of the proposed method is illustrated with bivariate LGCP simulations and a real data analysis of a bivariate point parttern of the 2014 terrorist attacks in Nigeria retrieved from the Global Terrorism Database.