Inference for means and covariances of point processes through estimating functions

Liang & Zeger (1986) introduced methodology for the analysis of longitudina l data that provides an alternative to likelihood-based inference. They con sidered modelling the marginal means of the response follow-up measures, an d proposed the use of unbiased estimating functions to handle inference. He re we wish to do the same for point or jump processes. We consider parametr ic models for the marginal means, and possibly the covariance structures, o f processes that allow covariates. Inference is performed with unbiased est imating functions and robust variance estimates are provided. The optimal l inear estimating function is presented in general. The special case of mixe d Poisson processes is discussed in further detail with an asymptotic effic iency study and simulations.