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Adjusted composite likelihood ratio test for spatial Gibbs point processes

by Adrian Baddeley, Rolf Turner and Ege Rubak
CSGB Research Reports Number 13 (November 2014)

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 $\chi^2$ 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 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 data.

Keywords Georgii-Nguyen-Zessin formula; Godambe-Heyde criterion; Moment matching; Papangelou conditional intensity; Pseudolikelihood; Score test statistic; Variance estimation.

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