Inference for means and covariances of point processes through estimating functions

Abstract

SUMMARY Liang & Zeger (1986) introduced methodology for the analysis of longitudinal data that provides an alternative to likelihood-based inference. They considered modelling the marginal means of the response follow-up measures, and proposed the use of unbiased estimating functions to handle inference. Here we wish to do the same for point or jump processes. We consider parametric models for the marginal means, and possibly the covariance structures, of processes that allow covariates. Inference is performed with unbiased estimating functions and robust variance estimates are provided. The optimal linear estimating function is presented in general. The special case of mixed Poisson processes is discussed in further detail with an asymptotic efficiency study and simulations.