Adjusted composite likelihood ratio test for spatial Gibbs point processes. Issue 5 (23rd March 2016)

• Record Type: Journal Article
• Authors: Baddeley, Adrian; Turner, Rolf; Rubak, Ege
• Is Part Of: Journal of statistical computation and simulation. Volume 86:Issue 5(2016)
• Page Start: 922
• Page End: 941
• Publication Date: 2016-03-23
• Subjects: Georgii–Nguyen–Zessin formula -- Godambe–Heyde criterion -- moment matching -- Papangelou conditional intensity -- pseudolikelihood -- score test statistic -- variance estimation; Primary: 62F03 -- Secondary: 62M30 -- 60G55 -- 62-07; Mathematical statistics -- Data processing -- Periodicals; Digital computer simulation -- Periodicals; 519.5028505
• DOI: 10.1080/00949655.2015.1044530
• Languages: English
• ISSNs: 0094-9655

Abstract

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 χ 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 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.