Quasi-likelihood for spatial point processes

• 成果类型: Article
• 署名作者: Guan, Yongtao; Jalilian, Abdollah; Waagepetersen, Rasmus
• 署名单位: University of Miami; Razi University; Aalborg University
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12083
• 发表日期: 2015
• 页码: 677-697
• 关键词: GENERALIZED LINEAR-MODELS; estimating equations; cox processes; patterns; intensity; inference; variance

摘要

Fitting regression models for intensity functions of spatial point processes is of great interest in ecological and epidemiological studies of association between spatially referenced events and geographical or environmental covariates. When Cox or cluster process models are used to accommodate clustering that is not accounted for by the available covariates, likelihoodbased inference becomes computationally cumbersome owing to the complicated nature of the likelihood function and the associated score function. It is therefore of interest to consider alternative, more easily computable estimating functions. We derive the optimal estimating function in a class of first-order estimating functions. The optimal estimating function depends on the solution of a certain Fredholm integral equation which in practice is solved numerically. The derivation of the optimal estimating function has close similarities to the derivation of quasi-likelihood for standard data sets. The approximate solution is further equivalent to a quasi-likelihood score for binary spatial data. We therefore use the term quasi-likelihood for our optimal estimating function approach. We demonstrate in a simulation study and a data example that our quasi-likelihood method for spatial point processes is both statistically and computationally efficient.