Adjusted composite likelihood ratio test for spatial Gibbs point processes

Abstract

We investigate an analogue of the likelihood ratio test for spatial Gibbs point process models fitted by maximum pseudolikelihood or maximum composite likelihood. The test statistic must be adjusted in order to obtain an asymptotic distribution under the null hypothesis. Adjustments developed for composite likelihoods of finite systems of random variables are adapted to the point process setting. Recent results in point process theory are used to estimate the composite information J and sensitivity H from the point pattern data. In a large simulation experiment we find that the proposed test is exact if J and H are known exactly; it is slightly conservative when J and H are estimated from the data.