A0617
Title: Composite likelihood inference for space-time point processes
Authors: Abdollah Jalilian - Razi University (Iran)
Francisco Cuevas - Universidad Técnica Federico Santa María (Chile)
Ganggang Xu - University of Miami (United States) [presenting]
Rasmus Waagepetersen - Aalborg University (Denmark)
Abstract: The dynamics of a rain forest are extremely complex, involving births, deaths, and growth of trees with complex interactions between trees, animals, climate, and environment. The patterns of recruits (new trees) and dead trees are considered between rainforest censuses. For the current census, regression models are specified for the conditional intensity of recruits and the conditional probabilities of death given the current trees and spatial covariates. Regression parameters are estimated using conditional composite likelihood functions that only involve the conditional first-order properties of the data. When constructing assumption-lean estimators of covariance matrices of parameter estimates, mild assumptions of decaying conditional correlations in space are only needed, while assumptions regarding correlations over time are avoided by exploiting conditional centering of composite likelihood score functions. Time series of point patterns from rain forest censuses are quite short, while each point pattern covers a fairly big spatial region. To obtain asymptotic results, a central limit theorem is therefore used for the fixed timespan - increasing spatial domain asymptotic setting. This also allows handling the challenge of using stochastic covariates constructed from past point patterns. Conveniently, it suffices to impose weak dependence assumptions on the innovations of the space-time process.
