Quasi-likelihood for spatial point processes

Yongtao Guan, Abdollah Jalilian, Rasmus Waagepetersen

Research output: Contribution to journalArticle

14 Scopus citations

Abstract

Summary: 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.

Original languageEnglish (US)
Pages (from-to)677-697
Number of pages21
JournalJournal of the Royal Statistical Society. Series B: Statistical Methodology
Volume77
Issue number3
DOIs
StatePublished - Jun 1 2015

Keywords

  • Estimating function
  • Fredholm integral equation
  • Godambe information
  • Intensity function
  • Regression model
  • Spatial point process

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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